Probleme probas

Bemo52 · 07-11-2014 17:11:28

Salut,

On a une pièce de monnaie avec une face numérotée 0 et l'autre numérotée 1.
On se propose de lancer la pièce 100 fois.
On crée une suite horizontale de cases vides (au plus 100 cases).
On part de la case 1.
Si la pièce lancée affiche 0 on note 0 dans la case concernée et on passe à la suivante.
Si la pièce lancée affiche 1 on la relance une 2ème fois :
- si elle affiche 0 on note 0 dans la case concernée et on passe à la suivante
- si elle affiche 1 on note 1 dans la case concernée et on passe à la suivante.
On continue de cette façon jusqu’au 100ème lancer.
Après le dernier lancer on compte le nombre de fois que l'on a noté 1.
Essai 1 : par exemple : 25 fois 1.
On répète le processus 1000 fois (donc essai 1 à essai 1000).
Quelle est la distribution des valeurs attendue en termes de fréquences ?

Merci pour tout éclairage.

Bemo52 · 08-11-2014 16:23:10

Resalut,

Toujours pas de reponse?
La loi binomiale n`est pas la reponse a mon humble avis.
Je me suis deja engueule avec un mec a ce sujet.
Le seul moyen de verifier cela est la simulation.
J`attends vos avis d`experts en la matiere.

Merci

freddy · 08-11-2014 19:27:57

Bemo52 a écrit :

Resalut,
Toujours pas de reponse?
La loi binomiale n`est pas la reponse a mon humble avis (houla, t'en es capable? )
Je me suis deja engueule avec un mec a ce sujet.
Le seul moyen de verifier cela est la simulation.
J`attends vos avis d`experts en la matiere.
Merci

Salut,

C'est bien cela le problème avec toi, aucun respect pour personne. Du coup, ici, t'es un peu tricard tant que tu ne changeras pas d'attitude envers les intervenants.

Pour la solution sans simulation, il suffit de développer la fonction génératrice de chaque essai et de répéter mille fois l'expérience.

Je pose [tex]p = \Pr (0)[/tex] dont je ne connais pas la valeur puisqu'on a aucune hypothèse sur l'équilibre de la pièce et on a :

[tex]G_X=\left(p+(1-p)\times \left(p+(1-p)\times X\right)\right)^{100}=\left(p(2-p)+(1-p)^2X\right)^{100}[/tex]

Et comme on vérifie que : [tex]p(2-p) + (1-p)^2 =1[/tex], à mon très humble avis, c'est bien une [tex]\mathcal{B}(p(2-p),\, 100)[/tex]

Bemo52 · 08-11-2014 21:49:56

Merci pour cette reponse.
Je ne suis pas un tetu. Je ne manque de respect qu`envers ceux qui repondent sans avoir lu l`enonce ou poser les questions de clarification necessaires. Je ne suis pas venu pour un devoir. Je viens pour poser des questions limite-limite.
La piece est juste (fair comme disent les anglais).
La probabilite d`avoir un zero est egal a 1/2.
Il y a un probleme quand meme qui montre que l`on n`a pas lu l`enonce.
Imaginons le 99 eme lancer. On obtient 0 on note 0 dans la kieme case et on passe a la kieme + 1.
On lance la piece on obtient un 1. On est oblige de lancer la piece la 101 eme fois. On fait quoi?
On note quoi dans k+1 eme case?
J`aurais aime que la loi binomiale s`applique mon probleme serait plus simple.

Cela dit, merci.

freddy · 08-11-2014 21:55:55

Re,

tu vois, le problème est que ton énoncé est incomplet (pour ne pas dire pas clair). Donc les réponses ne peuvent pas être celles que tu attends.
Je ne vois pas où tu as dis que chaque lancer donnait le numéro de la case à remplir. Si l'énigme réside déjà dans la compréhension du sujet, moi je dis "Basta !"
Quand on veut être compris, il y a un truc magique : on donne un exemple simple.
Perso, je passe la main.

Bemo52 · 08-11-2014 21:57:22

La valeur maximale est 50. Soit 100 fois 1 a chaque lancer. Donc elle correspond a une suite unique.
La valeur minimale est zero. Elle correspond a des millions de lancers differents (je ne les ai pas calculees ).

Bemo52 · 08-11-2014 22:00:19

freddy a écrit :

Re,
tu vois, le problème est que ton énoncé est incomplet (pour ne pas dire pas clair). Donc les réponses ne peuvent pas être celles que tu attends.
Je ne vois pas où tu as dis que chaque lancer donnait le numéro de la case à remplir. Si l'énigme réside déjà dans la compréhension du sujet, moi je dis "Basta !"
Quand on veut être compris, il y a un truc magique : on donne un exemple simple.
Perso, je passe la main.

C`est clair si tu lisais l`enonce.
On lance : si c`est 0 on note 0 et on passe a la case suivante.
Si c`est 1 on relance la piece une seconde fois : 0 on note zero et on passe a la case suivante, 1 on note 1 et on passe a la case suivante.
Relis l`enonce.

Bemo52 · 08-11-2014 22:01:21

Je me recite :

"Si la pièce lancée affiche 0 on note 0 dans la case concernée et on passe à la suivante.
Si la pièce lancée affiche 1 on la relance une 2ème fois :
- si elle affiche 0 on note 0 dans la case concernée et on passe à la suivante
- si elle affiche 1 on note 1 dans la case concernée et on passe à la suivante"

Bemo52 · 09-11-2014 00:33:28

En prenant 10 lancers par exemple la probabilite que X soit <=5 est de 100%. La valeur maximale est 5. Elle correspond aux resultats : 1111111111
Avec les parametres donnes par toi (3/4,10) je n`obtiens pas 100%.
Il y a un probleme evident donc.
La loi binomiale ne s`applique pas a mon cas.
Je vais poster les valeurs exactes pour 10 lancers juste pour prouver que vous avez tort.

tibo · 09-11-2014 01:01:21

Salut,

Bemo52 a écrit :

Je ne manque de respect qu`envers ceux qui repondent sans avoir lu l`enonce ou poser les questions de clarification necessaires.

Il peut arriver à tout le monde, sauf toi bien entendu, de mal lire ou mal comprendre un énoncé (surtout lorsque qu'un énoncé est aussi mal posé que le tien...). Je n'y vois pas là une raison de manquer de respect à tes lecteurs. (D'ailleurs je ne vois aucune raison qui autorise de manquer de respect à quelqu'un.)

Bemo52 a écrit :

Il y a un probleme quand meme qui montre que l`on n`a pas lu l`enonce.
Imaginons le 99 eme lancer. On obtient 0 on note 0 dans la kieme case et on passe a la kieme + 1.
On lance la piece on obtient un 1. On est oblige de lancer la piece la 101 eme fois. On fait quoi?
On note quoi dans k+1 eme case?

Bah c'est toi qui a posté le sujet, il me semble que c'est à toi de répondre à ces questions non? Si toi même ne comprend pas ce que tu écris, je ne vois pas comment nous, pauvres mortels, pourrait-on comprendre.

Je vais tout de même essayer:

Bemo52 a écrit :

On continue de cette façon jusqu’au 100ème lancer.

Je comprend cette phrase comme "Peu importe le résultat du 100ième lancer, on s’arrête.".

Et voici un énoncé qui me semble équivalent :
"On lance 100 fois une pièce parfaitement équilibrée avec ses faces notées PILE et FACE.
Soit X la variable aléatoire qui compte le nombre de fois que l'on obtient deux PILE d'affilé, sans que ces couples de PILE ne se chevauchent. Par exemple, si l'on a trois PILE d'affilé, on ne compte qu'une fois.
Déterminer la loi de probabilité de X"

J'ai déjà vu ça quelque part. Si je retrouve, je le dirai.

Dernière modification par tibo (09-11-2014 01:04:50)

yoshi · 09-11-2014 13:19:25

Salut,

Post #2,Bemo a écrit :

a écrit :
Toujours pas de reponse ?

J'ai déjà fait remarquer à nombre de contributeurs que ce genre de procédé n'était pas admis ici, c'est une forme de flood, voire de harcèlement..
Et si 8 jours après, tu n'avais pas eu de réponse, on aurait eu à droit à 8 rappels ?
Tu es prié d'attendre patiemment ladite réponse, s'il doit y en avoir.
Dans le cas contraire, cela signifierait que soit ton sujet n'intéresse personne, soit que personne n'a de réponse...

Tu voulais souhaitais une simulation ?
Voilà...
J'ai programmé ainsi :
Lancer n° i avec 1≤i≤100
Préparer un casier vide de 1000 cases (pour les résultats de chaque séquence de 100)
Faire 1000 fois
Partir d'un casier vide de 100 cases
Faire 100 fois
Lancer de pièce
Si face=0
j'inscris 0 dans la 1ere case vide
Sinon
je relance la pièce
j'inscris le résultat dans cette 1ere case vide
fin des 100 lancers
Je stocke l'un après l'autre les couples (nombre de 0, nombre de 1) dans le casier Simulation
fin des 1000 fois

J'affiche mes 1000 couples

C'est bien cela :
(je remplis mes casiers de la gauche vers la droite)
tirage n° i (avec [tex]1\leq i \leq 100)[/tex]
si tirage = 0, je j'inscris dans la 1ere non vide (en partant de la gauche) et j'avance
si tirage = 1, je procède à un 2e essai et quel que soit ce résultat, je l'inscris dans la 1ere case vide.

Si c'est le cas, j'ai reprogrammé, voilà tes 1000 essais :
[(45, 20), (33, 27), (56, 15), (42, 24), (47, 19), (52, 15), (43, 23), (50, 18), (43, 23), (47, 19), (46, 20), (45, 22), (52, 15), (48, 16), (51, 16), (52, 16), (46, 20), (53, 17), (49, 18), (50, 14), (57, 10), (52, 14), (45, 18), (44, 21), (47, 18), (53, 15), (45, 19), (47, 18), (50, 17), (54, 15), (49, 15), (56, 11), (43, 24), (57, 11), (46, 18), (52, 16), (57, 13), (51, 16), (58, 12), (55, 13), (41, 23), (54, 16), (50, 17), (48, 17), (46, 20), (45, 20), (47, 19), (51, 20), (48, 16), (60, 12), (49, 16), (58, 13), (55, 16), (42, 21), (55, 18), (54, 15), (59, 13), (51, 16), (52, 16), (49, 19), (56, 12), (51, 18), (51, 17), (58, 13), (40, 26), (45, 22), (58, 16), (52, 18), (49, 19), (58, 11), (51, 16), (53, 14), (56, 12), (42, 22), (63, 11), (60, 9), (44, 21), (57, 15), (41, 21), (42, 19), (48, 17), (49, 21), (53, 14), (63, 10), (55, 15), (62, 12), (57, 12), (56, 15), (57, 14), (47, 18), (56, 16), (51, 16), (51, 15), (47, 19), (49, 20), (54, 16), (53, 18), (53, 12), (50, 20), (48, 17), (46, 17), (35, 25), (48, 20), (48, 17), (55, 13), (51, 17), (49, 20), (54, 14), (51, 17), (53, 17), (55, 14), (49, 19), (48, 18), (50, 19), (50, 14), (48, 16), (48, 21), (46, 20), (49, 18), (53, 16), (52, 15), (51, 16), (53, 15), (40, 21), (48, 19), (62, 11), (49, 17), (53, 16), (49, 19), (46, 19), (50, 17), (50, 18), (54, 15), (54, 18), (52, 17), (49, 16), (43, 21), (53, 16), (51, 17), (55, 13), (54, 17), (52, 16), (48, 16), (46, 21), (57, 14), (46, 19), (58, 16), (53, 14), (54, 13), (58, 14), (41, 21), (50, 19), (58, 15), (52, 16), (51, 17), (51, 14), (54, 12), (43, 20), (52, 16), (53, 16), (46, 18), (54, 13), (48, 19), (61, 13), (49, 21), (41, 24), (39, 22), (44, 22), (56, 12), (42, 23), (52, 17), (55, 14), (47, 18), (53, 16), (48, 17), (58, 11), (46, 19), (48, 19), (44, 20), (48, 18), (47, 20), (48, 19), (45, 19), (50, 16), (51, 16), (56, 14), (56, 14), (52, 13), (48, 20), (46, 19), (57, 15), (56, 13), (51, 17), (59, 13), (51, 12), (51, 16), (57, 14), (45, 22), (56, 12), (46, 19), 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(56, 15), (51, 13), (47, 19), (51, 16), (54, 15), (50, 16), (50, 18), (46, 18), (48, 19), (53, 15), (39, 23), (54, 15), (50, 19), (55, 16), (62, 11), (50, 19), (50, 16), (52, 16), (49, 20), (54, 17), (47, 20), (52, 15), (55, 13), (55, 15), (53, 15), (49, 17), (54, 16), (50, 17), (52, 15), (55, 14), (48, 19), (51, 18), (51, 17), (48, 18), (52, 16), (53, 17), (57, 14), (53, 16), (49, 15), (46, 21), (54, 16), (43, 22), (52, 17), (45, 21), (51, 16), (50, 15), (50, 15), (49, 19), (45, 20), (52, 16), (57, 13), (53, 17), (49, 17), (50, 16), (59, 12), (54, 17), (50, 16), (59, 11), (62, 8), (46, 18), (48, 18), (50, 18), (50, 19), (57, 12), (59, 11), (43, 17), (52, 18), (46, 21), (51, 16), (46, 18), (54, 15), (52, 14), (49, 18), (50, 18), (48, 21), (59, 15), (52, 18), (56, 14), (46, 22), (46, 18), (58, 12), (60, 11), (50, 19), (56, 16), (50, 19), (50, 17), (54, 15), (55, 12), (52, 15), (60, 13), (47, 18), (52, 17), (57, 11), (49, 17), (43, 20), (56, 14), (47, 19), (49, 19), (50, 17), (54, 16), (62, 11), (47, 20), (48, 19), (47, 15), (56, 15), (48, 16), (53, 16), (49, 20), (47, 20), (49, 20), (62, 9), (49, 16), (50, 17), (50, 18), (44, 22), (43, 20), (43, 19), (49, 15), (56, 17), (45, 18), (46, 16), (50, 13), (61, 12), (52, 18), (51, 17), (54, 18), (56, 15), (55, 12), (49, 18), (50, 15), (54, 16), (44, 22), (48, 19), (56, 12), (47, 17), (48, 17), (52, 15), (50, 17), (47, 21), (60, 11), (50, 17), (38, 25), (52, 14), (54, 17), (55, 15), (60, 11), (57, 13), (55, 13), (56, 14), (55, 13), (48, 18), (53, 15), (43, 21), (54, 16), (43, 22), (46, 22), (58, 11), (39, 25), (54, 15), (49, 20), (47, 18), (50, 16), (52, 14), (49, 16), (54, 16), (46, 18), (53, 13), (52, 15), (53, 16), (51, 18), (50, 18), (51, 16), (53, 14), (51, 17), (42, 23), (48, 18), (53, 15), (60, 10), (52, 16), (47, 19), (55, 14), (54, 15), (51, 14), (50, 15), (48, 18), (50, 17), (51, 15), (44, 21), (43, 23), (58, 10), (56, 15), (45, 18), (47, 18), (43, 17), (44, 21), (51, 17), (50, 17), (50, 15), (46, 19), (45, 21), (53, 15), (56, 13), (53, 13), (49, 17), (54, 11), (59, 11), (53, 15), (50, 18), (46, 20), (54, 15), (52, 17), (56, 13), (51, 18), (52, 13), (44, 22), (43, 20), (54, 13), (50, 16), (45, 21), (45, 17), (53, 16), (58, 15), (49, 16), (40, 23), (52, 17), (56, 12), (57, 13), (50, 15), (55, 16), (55, 15), (48, 19), (51, 18), (57, 15), (56, 15), (54, 15), (57, 13), (55, 11), (43, 22), (52, 18), (52, 16), (50, 16), (42, 19), (54, 18), (49, 18), (54, 17), (43, 25), (51, 18), (44, 19), (49, 18), (44, 20), (49, 15), (54, 14), (50, 17), (59, 15), (56, 14), (41, 24), (39, 24), (57, 15), (55, 15), (53, 15), (68, 3), (49, 19), (49, 15), (54, 15), (51, 14), (59, 14), (58, 12), (46, 22), (45, 24), (61, 13), (54, 17), (52, 15), (51, 18), (44, 21), (50, 18), (50, 16), (43, 24), (53, 19), (46, 21), (48, 17), (55, 17), (46, 19), (53, 16), (48, 20), (45, 21), (52, 13), (50, 18), (53, 14), (57, 13), (46, 20), (54, 14), (41, 27), (49, 16), (52, 16), (48, 19), (58, 12), (50, 18), (51, 15), (50, 20), (59, 13), 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15)]

Attention, les générateurs aléatoire d'ordinateur ne sont que "pseudo-aléatoires"...

Les couples sont les sorties globales de 0 et de 1.
C'est suffisant ou tu veux les plus longues suites de 0 ou de 1 consécutives ?

@+

Bemo52 · 09-11-2014 18:50:32

Merci beaucoup pour toutes ces donnees.
Les resultats vont dans le bon sens.
Desole pour le "harcelement".
Je retourne a mon gourbi.

Bemo52 · 09-11-2014 21:14:02

Resalut,

Meme probleme avec une variante :

Si la pièce lancée affiche 0 on note 0 dans la case concernée et on passe à la suivante.
Si la pièce lancée affiche 1 on la relance une 2ème fois :
- si elle affiche 0 on note -1 dans la case concernée et on passe à la suivante
- si elle affiche 1 on note 1 dans la case concernée et on passe à la suivante

Au fur et a mesure on cumule les -1 et les +1 a l`aide d`une fonction sommatoire.

On effectue toujours les lancers par 100. On arrete une fois les 100 lancers atteints et on note la somme obtenue (negative ou positive ou nulle).

On refait la meme procedure durant 1000 essais.

En fait, ce petit probleme fait partie d`un autre plus large. J`expliquerai plus tard a quoi tout cela peut servir.

Je suis curieux de connaitre le resultat. J`ai fait une simulation sur tableur et ce qui me surprend c`est l`ampleur des variations.

Merci.

yoshi · 09-11-2014 21:28:30

Re,

Je stocke les triplets (nb de -1, nb de 0, nb de 1)
[(14, 28, 23), (16, 35, 17), (17, 22, 23), (21, 37, 11), (21, 35, 12), (12, 41, 18), (17, 31, 18), (18, 34, 16), (17, 32, 18), (19, 45, 9), (21, 26, 17), (16, 39, 15), (20, 37, 12), (18, 33, 16), (20, 33, 14), (15, 37, 17), (19, 31, 16), (17, 35, 16), (14, 42, 16), (20, 28, 17), (14, 33, 20), (15, 39, 16), (18, 35, 15), (14, 44, 15), (18, 34, 16), (14, 39, 17), (14, 39, 17), (21, 27, 16), (9, 39, 22), (18, 36, 15), (17, 33, 17), (16, 45, 12), (16, 37, 16), (18, 35, 15), (18, 31, 17), (15, 33, 19), (12, 29, 24), (8, 45, 20), (20, 31, 15), (17, 35, 16), (15, 29, 21), (21, 32, 14), (22, 33, 12), (16, 34, 18), (16, 30, 20), (19, 37, 13), (17, 33, 17), (14, 41, 16), (18, 27, 19), (19, 34, 15), (16, 39, 15), (10, 31, 25), (14, 40, 17), (21, 25, 17), (20, 23, 19), (14, 41, 16), (21, 27, 16), (18, 31, 17), (21, 31, 14), (15, 33, 19), (23, 22, 17), (19, 27, 18), (21, 37, 11), (24, 25, 14), (15, 41, 15), (19, 37, 13), (20, 27, 17), (18, 27, 19), (15, 37, 17), (20, 36, 13), (17, 40, 14), (18, 32, 17), (17, 37, 15), (20, 27, 17), (17, 28, 20), (18, 27, 19), (19, 37, 13), (13, 32, 22), (20, 31, 15), (16, 42, 14), (16, 29, 20), (17, 41, 13), (20, 30, 16), (20, 34, 14), (15, 31, 20), (14, 36, 19), (18, 28, 19), (17, 37, 15), (16, 27, 21), (24, 26, 14), (14, 45, 14), (13, 35, 20), (15, 35, 18), (20, 33, 14), (14, 27, 23), (16, 34, 18), (13, 33, 21), (19, 31, 16), (18, 30, 18), (14, 44, 15), (14, 36, 19), (21, 27, 16), (16, 48, 11), (15, 34, 19), (15, 35, 18), (19, 28, 18), (10, 28, 27), (17, 41, 13), (14, 37, 18), (12, 47, 15), (18, 31, 17), (17, 37, 15), (19, 34, 15), (21, 30, 15), (21, 29, 15), (16, 35, 17), (22, 34, 12), (18, 35, 15), (17, 33, 17), (20, 35, 13), (19, 30, 17), (19, 41, 11), (14, 41, 16), (13, 41, 17), (18, 43, 11), (15, 36, 18), (19, 31, 16), (15, 31, 20), (19, 25, 19), (21, 28, 16), (22, 35, 11), (19, 32, 16), (15, 35, 18), (15, 35, 18), (16, 30, 20), (22, 21, 18), (21, 32, 14), (21, 41, 9), (17, 41, 13), (22, 23, 17), (17, 25, 21), (20, 39, 11), (22, 28, 15), (21, 31, 14), (13, 33, 21), (18, 29, 18), (17, 39, 14), (17, 28, 20), (14, 35, 19), (16, 37, 16), (18, 37, 14), (16, 31, 19), (10, 45, 18), (18, 33, 16), (17, 36, 16), (12, 30, 24), (20, 25, 18), (15, 37, 17), (12, 34, 22), (21, 31, 14), (11, 38, 21), (18, 41, 12), (15, 34, 19), (13, 29, 23), (15, 37, 17), (14, 45, 14), (17, 30, 19), (15, 27, 22), (11, 38, 21), (13, 43, 16), (12, 31, 23), (21, 29, 15), (22, 37, 10), (20, 31, 15), (25, 25, 13), (18, 44, 11), (22, 33, 12), (19, 23, 20), (15, 33, 19), (18, 38, 14), (19, 31, 16), (22, 27, 15), (15, 31, 20), (21, 29, 15), (22, 29, 14), (22, 22, 18), (19, 33, 15), (20, 30, 16), (16, 32, 19), (16, 37, 16), (17, 39, 14), (22, 24, 17), (11, 35, 22), (17, 29, 19), (17, 35, 16), (20, 35, 13), (21, 30, 15), (16, 43, 13), (25, 23, 14), (15, 35, 18), (18, 22, 22), (8, 35, 25), (13, 38, 19), (16, 26, 22), (13, 35, 20), (19, 30, 17), (16, 28, 21), (15, 38, 17), (14, 32, 21), (21, 21, 19), (18, 32, 17), (21, 36, 12), (21, 35, 12), (10, 44, 19), (17, 33, 17), (25, 31, 10), (17, 33, 17), (20, 35, 13), (19, 33, 15), (20, 27, 17), (17, 29, 19), (18, 36, 15), (19, 38, 13), (16, 31, 19), (18, 34, 16), (19, 36, 14), (16, 26, 22), (13, 39, 18), (14, 31, 21), (13, 45, 15), (20, 41, 10), (17, 32, 18), (19, 40, 12), (16, 51, 9), (13, 32, 22), (22, 25, 16), (18, 40, 13), (13, 37, 19), (16, 45, 12), (18, 25, 20), (23, 29, 13), (9, 43, 20), (15, 36, 18), (15, 32, 20), (16, 39, 15), (18, 30, 18), (19, 31, 16), (16, 30, 20), (15, 36, 18), (13, 51, 12), (14, 29, 22), (19, 39, 12), (8, 31, 27), (14, 33, 20), (24, 34, 10), (17, 27, 20), (19, 38, 13), (15, 31, 20), (21, 36, 12), (17, 37, 15), (16, 39, 15), (13, 36, 20), (17, 29, 19), (18, 35, 15), (15, 45, 13), (24, 34, 10), (17, 24, 22), (15, 37, 17), (20, 25, 18), (15, 32, 20), (11, 40, 20), (21, 30, 15), (18, 35, 15), (16, 31, 19), (18, 31, 17), (15, 33, 19), (19, 23, 20), (18, 31, 17), (15, 30, 21), (19, 38, 13), (15, 29, 21), (16, 35, 17), (16, 38, 16), (18, 35, 15), (9, 39, 22), (12, 36, 21), (16, 33, 18), (16, 38, 16), (20, 28, 17), (21, 32, 14), (17, 30, 19), (13, 35, 20), (15, 32, 20), (15, 31, 20), (16, 30, 20), (12, 35, 21), (17, 29, 19), (16, 42, 14), (15, 36, 18), (14, 34, 20), (16, 41, 14), (16, 28, 21), (14, 43, 15), (19, 25, 19), (16, 38, 16), (19, 39, 12), (20, 35, 13), (19, 37, 13), (20, 29, 16), (20, 31, 15), (15, 32, 20), (16, 30, 20), (19, 27, 18), (16, 33, 18), (21, 33, 13), (15, 39, 16), (20, 30, 16), (18, 32, 17), (15, 38, 17), (14, 34, 20), (15, 33, 19), (13, 38, 19), (22, 34, 12), (17, 27, 20), (16, 37, 16), (15, 35, 18), (18, 37, 14), (20, 27, 17), (17, 35, 16), (15, 34, 19), (13, 41, 17), (13, 28, 24), (8, 45, 20), (20, 33, 14), (20, 35, 13), (13, 34, 21), (17, 31, 18), (18, 24, 21), (15, 29, 21), (22, 27, 15), (18, 21, 22), (19, 33, 15), (12, 44, 17), (19, 33, 15), (18, 38, 14), (15, 35, 18), (15, 35, 18), (20, 35, 13), (14, 35, 19), (13, 41, 17), (16, 33, 18), (13, 39, 18), (15, 30, 21), (12, 45, 16), (13, 34, 21), (13, 40, 18), (25, 31, 10), (16, 32, 19), (16, 35, 17), (18, 31, 17), (11, 36, 22), (17, 37, 15), (14, 40, 17), (12, 39, 19), (16, 35, 17), (18, 30, 18), (19, 33, 15), (17, 34, 17), (18, 29, 18), (13, 37, 19), (18, 26, 20), (11, 42, 19), (16, 27, 21), (10, 34, 24), (13, 33, 21), (14, 32, 21), (16, 41, 14), (15, 39, 16), (22, 23, 17), (20, 32, 15), (15, 31, 20), (17, 32, 18), (18, 31, 17), (17, 39, 14), (15, 33, 19), (14, 41, 16), (13, 42, 17), (12, 31, 23), (18, 29, 18), (15, 25, 23), (15, 22, 25), (18, 35, 15), (13, 35, 20), (18, 32, 17), (18, 31, 17), (15, 31, 20), (15, 35, 18), (16, 36, 17), (9, 43, 20), (16, 37, 16), (17, 30, 19), (23, 26, 15), (16, 28, 21), (21, 40, 10), (18, 25, 20), (10, 39, 21), (14, 39, 17), (12, 34, 22), (17, 39, 14), (16, 25, 22), (20, 27, 17), (18, 39, 13), (20, 35, 13), (13, 33, 21), (12, 31, 23), (12, 36, 21), (12, 50, 14), (16, 31, 19), (16, 41, 14), (15, 20, 26), (18, 27, 19), (19, 29, 17), (19, 33, 15), (11, 35, 22), (17, 41, 13), (15, 32, 20), (20, 37, 12), (21, 29, 15), (18, 36, 15), (13, 33, 21), (22, 24, 17), (16, 39, 15), (16, 39, 15), (19, 30, 17), (23, 31, 12), (17, 35, 16), (11, 36, 22), (15, 43, 14), (11, 40, 20), (18, 26, 20), (20, 40, 11), (16, 35, 17), (21, 24, 18), (21, 35, 12), (20, 29, 16), (18, 46, 10), (13, 48, 14), (21, 39, 10), (17, 27, 20), (17, 31, 18), (21, 29, 15), (21, 29, 15), (20, 28, 17), (17, 35, 16), (18, 27, 19), (17, 32, 18), (14, 38, 18), (12, 36, 21), (16, 27, 21), (20, 30, 16), (12, 46, 16), (20, 31, 15), (15, 32, 20), (16, 35, 17), (24, 29, 12), (20, 30, 16), (18, 35, 15), (21, 33, 13), (14, 43, 15), (14, 38, 18), (23, 22, 17), (17, 34, 17), (15, 36, 18), (17, 36, 16), (16, 39, 15), (15, 37, 17), (16, 39, 15), (18, 27, 19), (21, 23, 18), (15, 35, 18), (14, 34, 20), (20, 29, 16), (15, 38, 17), (16, 33, 18), (15, 29, 21), (16, 41, 14), (19, 29, 17), (16, 29, 20), (14, 32, 21), (17, 35, 16), (20, 31, 15), (19, 37, 13), (13, 39, 18), (21, 30, 15), (18, 30, 18), (17, 29, 19), (17, 39, 14), (11, 39, 20), (25, 24, 14), (20, 31, 15), (25, 29, 11), (17, 35, 16), (14, 34, 20), (8, 31, 27), (14, 36, 19), (20, 33, 14), (18, 30, 18), (15, 36, 18), (13, 30, 23), (15, 27, 22), (21, 33, 13), (24, 33, 10), (20, 33, 14), (25, 30, 11), (16, 30, 20), (19, 25, 19), (14, 26, 24), (16, 46, 12), (14, 30, 22), (17, 33, 17), (14, 31, 21), (16, 35, 17), (18, 33, 16), (23, 27, 14), (21, 25, 17), (19, 36, 14), (13, 41, 17), (13, 36, 20), (10, 33, 24), (19, 41, 11), (18, 29, 18), (20, 25, 18), (14, 28, 23), (18, 33, 16), (12, 29, 24), (21, 27, 16), (22, 31, 13), (20, 29, 16), (18, 42, 12), (17, 31, 18), (16, 33, 18), (17, 37, 15), (15, 33, 19), (20, 35, 13), (18, 29, 18), (18, 34, 16), (21, 25, 17), (19, 41, 11), (13, 51, 12), (15, 37, 17), (22, 41, 8), (19, 26, 19), (16, 32, 19), (19, 33, 15), (14, 38, 18), (18, 43, 11), (18, 41, 12), (19, 36, 14), (12, 40, 19), (23, 19, 18), (12, 41, 18), (17, 31, 18), (12, 35, 21), (16, 35, 17), (16, 36, 17), (19, 31, 16), (21, 31, 14), (22, 26, 16), (18, 23, 21), (19, 29, 17), (14, 31, 21), (16, 39, 15), (23, 27, 14), (20, 37, 12), (24, 29, 12), (18, 36, 15), (18, 38, 14), (15, 45, 13), (18, 31, 17), (14, 35, 19), (14, 41, 16), (21, 29, 15), (12, 43, 17), (13, 44, 16), (14, 38, 18), (18, 34, 16), (12, 37, 20), (18, 35, 15), (18, 33, 16), (23, 21, 17), (19, 31, 16), (18, 34, 16), (11, 47, 16), (20, 31, 15), (16, 39, 15), (22, 26, 16), (17, 33, 17), (17, 35, 16), (16, 35, 17), (11, 33, 23), (13, 32, 22), (20, 39, 11), (23, 37, 9), (22, 29, 14), (16, 34, 18), (16, 42, 14), (17, 27, 20), (20, 34, 14), (20, 40, 11), (17, 34, 17), (18, 37, 14), (20, 40, 11), (21, 26, 17), (17, 28, 20), (17, 35, 16), (14, 44, 15), (18, 33, 16), (16, 39, 15), (23, 35, 10), (15, 35, 18), (14, 34, 20), (14, 38, 18), (12, 33, 22), (14, 29, 22), (15, 37, 17), (19, 34, 15), (18, 35, 15), (16, 30, 20), (16, 37, 16), (17, 32, 18), (20, 31, 15), (24, 27, 13), (17, 38, 15), (16, 35, 17), (17, 40, 14), (13, 29, 23), (22, 33, 12), (16, 27, 21), (17, 31, 18), (17, 43, 12), (18, 31, 17), (19, 38, 13), (13, 33, 21), (20, 30, 16), (17, 37, 15), (19, 30, 17), (16, 34, 18), (15, 31, 20), (11, 41, 19), (22, 32, 13), (12, 36, 21), (14, 32, 21), (12, 41, 18), (9, 45, 19), (22, 25, 16), (13, 34, 21), (18, 29, 18), (22, 34, 12), (22, 31, 13), (17, 43, 12), (13, 35, 20), (15, 39, 16), (17, 41, 13), (14, 38, 18), (12, 29, 24), (20, 32, 15), (17, 33, 17), (19, 32, 16), (14, 39, 17), (20, 30, 16), (21, 46, 7), (24, 23, 15), (12, 31, 23), (19, 21, 21), (17, 38, 15), (20, 31, 15), (11, 40, 20), (23, 33, 11), (21, 30, 15), (22, 31, 13), (17, 33, 17), (16, 33, 18), (16, 34, 18), (16, 33, 18), (17, 43, 12), (16, 37, 16), (16, 25, 22), (22, 33, 12), (24, 29, 12), (15, 31, 20), (17, 33, 17), (14, 37, 18), (16, 32, 19), (15, 38, 17), (14, 45, 14), (14, 35, 19), (17, 30, 19), (14, 31, 21), (18, 33, 16), (16, 28, 21), (18, 35, 15), (22, 25, 16), (19, 24, 20), (13, 34, 21), (15, 38, 17), (17, 33, 17), (15, 34, 19), (17, 38, 15), (19, 35, 14), (17, 37, 15), (15, 35, 18), (18, 44, 11), (8, 39, 23), (21, 38, 11), (20, 37, 12), (22, 33, 12), (21, 31, 14), (15, 42, 15), (16, 33, 18), (16, 38, 16), (19, 25, 19), (14, 36, 19), (18, 31, 17), (19, 31, 16), (12, 41, 18), (23, 31, 12), (15, 35, 18), (18, 33, 16), (20, 34, 14), (16, 31, 19), (18, 32, 17), (11, 45, 17), (19, 24, 20), (13, 31, 22), (18, 39, 13), (16, 30, 20), (16, 39, 15), (20, 27, 17), (17, 32, 18), (12, 35, 21), (19, 34, 15), (18, 31, 17), (18, 36, 15), (21, 37, 11), (18, 29, 18), (15, 33, 19), (16, 39, 15), (20, 38, 12), (22, 28, 15), (15, 34, 19), (12, 38, 20), (14, 45, 14), (16, 38, 16), (17, 35, 16), (17, 27, 20), (19, 33, 15), (18, 38, 14), (12, 37, 20), (15, 27, 22), (20, 31, 15), (23, 30, 13), (19, 27, 18), (19, 33, 15), (13, 41, 17), (22, 28, 15), (25, 29, 11), (16, 36, 17), (19, 35, 14), (19, 30, 17), (19, 30, 17), (16, 37, 16), (14, 35, 19), (21, 36, 12), (15, 40, 16), (18, 35, 15), (19, 25, 19), (14, 42, 16), (23, 23, 16), (22, 27, 15), (18, 24, 21), (21, 23, 18), (18, 31, 17), (16, 39, 15), (23, 27, 14), (18, 33, 16), (22, 26, 16), (19, 31, 16), (13, 35, 20), (15, 33, 19), (18, 34, 16), (19, 31, 16), (15, 38, 17), (19, 44, 10), (19, 35, 14), (20, 30, 16), (14, 35, 19), (13, 41, 17), (17, 37, 15), (18, 39, 13), (24, 34, 10), (15, 42, 15), (15, 31, 20), (15, 35, 18), (15, 33, 19), (19, 35, 14), (20, 21, 20), (15, 32, 20), (12, 37, 20), (14, 37, 18), (13, 35, 20), (18, 37, 14), (17, 41, 13), (14, 39, 17), (21, 35, 12), (15, 40, 16), (18, 33, 16), (17, 27, 20), (17, 41, 13), (13, 41, 17), (16, 32, 19), (19, 27, 18), (16, 35, 17), (20, 34, 14), (18, 28, 19), (17, 37, 15), (15, 41, 15), (18, 25, 20), (14, 33, 20), (11, 41, 19), (14, 39, 17), (19, 30, 17), (17, 39, 14), (17, 33, 17), (20, 31, 15), (17, 33, 17), (16, 39, 15), (19, 44, 10), (18, 33, 16), (22, 27, 15), (17, 32, 18), (15, 33, 19), (14, 36, 19), (17, 28, 20), (20, 32, 15), (19, 37, 13), (16, 34, 18), (12, 38, 20), (17, 28, 20), (23, 30, 13), (15, 37, 17), (16, 33, 18), (21, 23, 18), (13, 36, 20), (18, 38, 14), (24, 29, 12), (18, 31, 17), (22, 26, 16), (20, 24, 19), (18, 37, 14), (14, 24, 25), (17, 30, 19), (16, 35, 17), (11, 49, 15), (19, 34, 15), (16, 33, 18), (15, 29, 21), (17, 35, 16), (14, 45, 14), (14, 31, 21), (17, 43, 12), (16, 34, 18), (15, 26, 23), (19, 33, 15), (18, 31, 17), (16, 39, 15), (20, 29, 16), (16, 35, 17), (12, 41, 18), (13, 33, 21), (17, 27, 20), (22, 29, 14), (13, 37, 19), (15, 28, 22), (14, 37, 18), (13, 31, 22), (15, 37, 17), (15, 30, 21), (15, 32, 20), (18, 29, 18), (19, 32, 16), (17, 30, 19), (19, 30, 17), (14, 39, 17), (16, 41, 14), (16, 38, 16), (24, 28, 13), (17, 37, 15), (15, 40, 16), (20, 31, 15), (17, 26, 21), (17, 38, 15), (11, 35, 22), (16, 34, 18), (21, 35, 12), (17, 33, 17), (19, 41, 11), (20, 41, 10), (16, 38, 16), (15, 36, 18), (18, 41, 12), (17, 35, 16), (14, 42, 16), (15, 42, 15), (21, 36, 12), (18, 39, 13), (12, 33, 22), (18, 36, 15), (14, 37, 18), (13, 35, 20), (16, 41, 14), (20, 27, 17), (18, 33, 16), (12, 41, 18), (14, 39, 17), (22, 34, 12), (16, 29, 20), (7, 41, 23), (17, 31, 18), (12, 40, 19), (16, 33, 18), (16, 27, 21), (20, 22, 20), (10, 44, 19), (17, 31, 18), (18, 39, 13), (16, 29, 20), (17, 32, 18), (20, 31, 15), (10, 33, 24), (16, 38, 16), (18, 27, 19), (16, 43, 13), (16, 36, 17), (15, 37, 17), (15, 36, 18), (20, 27, 17), (24, 28, 13), (19, 24, 20), (23, 25, 15), (15, 33, 19), (22, 31, 13), (13, 45, 15), (18, 34, 16), (15, 41, 15), (19, 39, 12), (16, 38, 16), (17, 33, 17), (17, 27, 20), (19, 27, 18), (19, 30, 17), (20, 25, 18), (18, 31, 17), (23, 31, 12), (14, 36, 19), (23, 29, 13), (18, 34, 16), (18, 31, 17), (17, 39, 14), (20, 20, 21), (21, 40, 10), (11, 31, 24), (21, 31, 14), (18, 26, 20), (18, 33, 16), (12, 33, 22), (14, 32, 21), (24, 24, 15), (16, 31, 19), (21, 34, 13), (14, 32, 21), (20, 27, 17), (22, 30, 14), (13, 39, 18), (14, 41, 16), (23, 36, 10), (19, 33, 15), (14, 34, 20), (13, 33, 21), (19, 34, 15), (20, 31, 15), (20, 30, 16), (16, 35, 17), (15, 41, 15), (14, 44, 15), (16, 39, 15), (19, 29, 17), (18, 23, 21), (16, 32, 19), (17, 33, 17), (22, 23, 17)]

1 min pour modifier mon prog
puis temps d'exécution/stockage de 1000 essais : de l'ordre de la s.
Je peux ne te donner que le résultat sec :
(14, 28, 23), (16, 35, 17), (17, 22, 23)
me donnent respectivement -14+23 = 9, -16+17=1, -17+23=6
J'ai pensé que ce serait plus intéressant comme ça...

Une 2e séquence de 1000 avec des quadruplets, j'ai ajouté le résultat :
[(18, 32, 17, -1), (13, 35, 20, 7), (18, 28, 19, 1), (20, 31, 15, -5), (21, 36, 12, -9), (19, 32, 16, -3), (16, 30, 20, 4), (17, 34, 17, 0), (14, 39, 17, 3), (15, 39, 16, 1), (24, 22, 16, -8), (22, 33, 12, -10), (14, 27, 23, 9), (25, 30, 11, -14), (15, 41, 15, 0), (18, 37, 14, -4), (21, 28, 16, -5), (14, 40, 17, 3), (18, 35, 15, -3), (17, 40, 14, -3), (22, 28, 15, -7), (17, 34, 17, 0), (16, 36, 17, 1), (16, 34, 18, 2), (11, 41, 19, 8), (16, 29, 20, 4), (16, 38, 16, 0), (16, 37, 16, 0), (9, 43, 20, 11), (15, 35, 18, 3), (26, 28, 11, -15), (15, 34, 19, 4), (12, 39, 19, 7), (13, 33, 21, 8), (19, 27, 18, -1), (10, 42, 20, 10), (15, 26, 23, 8), (21, 28, 16, -5), (15, 26, 23, 8), (18, 35, 15, -3), (16, 39, 15, -1), (16, 32, 19, 3), (15, 35, 18, 3), (12, 41, 18, 6), (22, 28, 15, -7), (14, 40, 17, 3), (17, 34, 17, 0), (17, 27, 20, 3), (16, 37, 16, 0), (17, 26, 21, 4), (18, 36, 15, -3), (20, 23, 19, -1), (18, 36, 15, -3), (15, 42, 15, 0), (9, 39, 22, 13), (18, 34, 16, -2), (16, 25, 22, 6), (18, 20, 23, 5), (23, 33, 11, -12), (20, 22, 20, 0), (14, 37, 18, 4), (21, 34, 13, -8), (17, 34, 17, 0), (21, 32, 14, -7), (20, 26, 18, -2), (13, 37, 19, 6), (23, 25, 15, -8), (16, 33, 18, 2), (20, 26, 18, -2), (23, 35, 10, -13), (14, 41, 16, 2), (11, 34, 23, 12), (18, 35, 15, -3), (16, 33, 18, 2), (14, 31, 21, 7), (25, 19, 16, -9), (14, 38, 18, 4), (18, 31, 17, -1), (15, 45, 13, -2), (16, 34, 18, 2), (13, 49, 13, 0), (18, 32, 17, -1), (21, 32, 14, -7), (22, 31, 13, -9), (20, 29, 16, -4), (15, 35, 18, 3), (23, 30, 13, -10), (15, 29, 21, 6), (20, 35, 13, -7), (17, 28, 20, 3), (23, 32, 12, -11), (17, 35, 16, -1), (16, 29, 20, 4), (17, 29, 19, 2), (14, 43, 15, 1), (17, 37, 15, -2), (16, 45, 12, -4), (12, 39, 19, 7), (23, 34, 11, -12), (16, 40, 15, -1), (16, 31, 19, 3), (19, 39, 12, -7), (19, 39, 12, -7), (18, 28, 19, 1), (14, 43, 15, 1), (15, 38, 17, 2), (12, 37, 20, 8), (18, 31, 17, -1), (17, 29, 19, 2), (18, 37, 14, -4), (22, 25, 16, -6), (18, 30, 18, 0), (10, 39, 21, 11), (15, 29, 21, 6), (14, 27, 23, 9), (15, 39, 16, 1), (17, 46, 11, -6), (15, 30, 21, 6), (14, 36, 19, 5), (10, 32, 25, 15), (13, 43, 16, 3), (15, 41, 15, 0), (17, 26, 21, 4), (16, 31, 19, 3), (17, 27, 20, 3), (15, 35, 18, 3), (15, 33, 19, 4), (11, 33, 23, 12), (17, 35, 16, -1), (15, 33, 19, 4), (14, 45, 14, 0), (19, 33, 15, -4), (15, 26, 23, 8), (13, 41, 17, 4), (19, 35, 14, -5), (18, 38, 14, -4), (12, 33, 22, 10), (16, 35, 17, 1), (19, 33, 15, -4), (14, 39, 17, 3), (17, 25, 21, 4), (14, 30, 22, 8), (16, 34, 18, 2), (24, 24, 15, -9), (18, 35, 15, -3), (18, 35, 15, -3), (12, 39, 19, 7), (17, 39, 14, -3), (16, 30, 20, 4), (17, 33, 17, 0), (21, 31, 14, -7), (16, 37, 16, 0), (16, 35, 17, 1), (15, 37, 17, 2), (19, 37, 13, -6), (18, 38, 14, -4), (18, 38, 14, -4), (15, 30, 21, 6), (14, 25, 24, 10), (20, 37, 12, -8), (16, 29, 20, 4), (14, 34, 20, 6), (14, 37, 18, 4), (19, 33, 15, -4), (16, 28, 21, 5), (15, 40, 16, 1), (16, 35, 17, 1), (15, 41, 15, 0), (17, 46, 11, -6), (17, 28, 20, 3), (18, 39, 13, -5), (19, 31, 16, -3), (21, 19, 20, -1), (20, 33, 14, -6), (17, 32, 18, 1), (15, 35, 18, 3), (19, 28, 18, -1), (21, 44, 8, -13), (13, 41, 17, 4), (16, 32, 19, 3), (17, 34, 17, 0), (19, 31, 16, -3), (15, 36, 18, 3), (15, 32, 20, 5), (19, 35, 14, -5), (16, 34, 18, 2), (17, 30, 19, 2), (15, 33, 19, 4), (17, 35, 16, -1), (12, 49, 14, 2), (16, 35, 17, 1), (11, 31, 24, 13), (18, 29, 18, 0), (12, 39, 19, 7), (21, 24, 18, -3), (21, 29, 15, -6), (11, 40, 20, 9), (17, 35, 16, -1), (20, 30, 16, -4), (16, 20, 25, 9), (16, 31, 19, 3), (14, 41, 16, 2), (21, 30, 15, -6), (18, 39, 13, -5), (21, 39, 10, -11), (21, 32, 14, -7), (21, 25, 17, -4), (21, 32, 14, -7), (21, 25, 17, -4), (21, 36, 12, -9), (14, 35, 19, 5), (12, 41, 18, 6), (18, 25, 20, 2), (12, 43, 17, 5), (12, 22, 28, 16), (16, 47, 11, -5), (21, 20, 20, -1), (17, 35, 16, -1), (20, 29, 16, -4), (13, 39, 18, 5), (12, 36, 21, 9), (17, 40, 14, -3), (18, 31, 17, -1), (21, 36, 12, -9), (26, 27, 11, -15), (11, 44, 18, 7), (19, 40, 12, -7), (12, 37, 20, 8), (22, 31, 13, -9), (16, 29, 20, 4), (13, 39, 18, 5), (11, 35, 22, 11), (23, 28, 14, -9), (15, 31, 20, 5), (19, 32, 16, -3), (17, 39, 14, -3), (18, 35, 15, -3), (21, 31, 14, -7), (20, 15, 23, 3), (17, 36, 16, -1), (13, 34, 21, 8), (19, 41, 11, -8), (16, 38, 16, 0), (17, 31, 18, 1), (18, 50, 8, -10), (18, 40, 13, -5), (20, 43, 9, -11), (18, 26, 20, 2), (17, 31, 18, 1), (19, 29, 17, -2), (18, 33, 16, -2), (17, 35, 16, -1), (16, 39, 15, -1), (16, 31, 19, 3), (14, 41, 16, 2), (19, 41, 11, -8), (13, 33, 21, 8), (19, 33, 15, -4), (16, 37, 16, 0), (18, 35, 15, -3), (15, 38, 17, 2), (19, 35, 14, -5), (24, 25, 14, -10), (19, 35, 14, -5), (20, 37, 12, -8), (11, 31, 24, 13), (21, 24, 18, -3), (20, 29, 16, -4), (23, 30, 13, -10), (21, 33, 13, -8), (15, 41, 15, 0), (15, 39, 16, 1), (16, 35, 17, 1), (14, 37, 18, 4), (17, 29, 19, 2), (16, 32, 19, 3), (21, 37, 11, -10), (18, 33, 16, -2), (13, 38, 19, 6), (18, 35, 15, -3), (19, 28, 18, -1), (24, 33, 10, -14), (17, 31, 18, 1), (19, 29, 17, -2), (16, 42, 14, -2), (14, 38, 18, 4), (12, 27, 25, 13), (15, 32, 20, 5), (14, 39, 17, 3), (12, 43, 17, 5), (13, 37, 19, 6), (16, 43, 13, -3), (14, 45, 14, 0), (18, 35, 15, -3), (19, 33, 15, -4), (16, 27, 21, 5), (20, 24, 19, -1), (19, 28, 18, -1), (18, 33, 16, -2), (17, 29, 19, 2), (17, 26, 21, 4), (18, 37, 14, -4), (14, 35, 19, 5), (16, 37, 16, 0), (11, 31, 24, 13), (24, 29, 12, -12), (13, 34, 21, 8), (15, 26, 23, 8), (23, 33, 11, -12), (13, 49, 13, 0), (16, 39, 15, -1), (16, 41, 14, -2), (13, 47, 14, 1), (19, 27, 18, -1), (19, 37, 13, -6), (11, 35, 22, 11), (22, 31, 13, -9), (21, 38, 11, -10), (22, 33, 12, -10), (13, 46, 15, 2), (10, 49, 16, 6), (19, 29, 17, -2), (19, 27, 18, -1), (17, 37, 15, -2), (16, 33, 18, 2), (18, 35, 15, -3), (22, 21, 18, -4), (19, 27, 18, -1), (10, 37, 22, 12), (16, 29, 20, 4), (17, 36, 16, -1), (21, 35, 12, -9), (19, 40, 12, -7), (27, 32, 8, -19), (13, 37, 19, 6), (12, 31, 23, 11), (25, 25, 13, -12), (18, 31, 17, -1), (18, 29, 18, 0), (17, 33, 17, 0), (20, 28, 17, -3), (18, 32, 17, -1), (13, 34, 21, 8), (14, 27, 23, 9), (13, 33, 21, 8), (16, 39, 15, -1), (20, 39, 11, -9), (20, 33, 14, -6), (15, 23, 24, 9), (17, 34, 17, 0), (11, 41, 19, 8), (19, 25, 19, 0), (19, 37, 13, -6), (13, 33, 21, 8), (19, 30, 17, -2), (22, 31, 13, -9), (22, 27, 15, -7), (16, 29, 20, 4), (20, 29, 16, -4), (21, 30, 15, -6), (22, 37, 10, -12), (12, 43, 17, 5), (18, 29, 18, 0), (19, 37, 13, -6), (18, 41, 12, -6), (15, 30, 21, 6), (17, 28, 20, 3), (13, 28, 24, 11), (19, 32, 16, -3), (15, 33, 19, 4), (19, 32, 16, -3), (16, 28, 21, 5), (23, 23, 16, -7), (18, 35, 15, -3), (15, 30, 21, 6), (14, 42, 16, 2), (16, 41, 14, -2), (22, 29, 14, -8), (15, 27, 22, 7), (19, 45, 9, -10), (14, 38, 18, 4), (15, 38, 17, 2), (20, 24, 19, -1), (9, 41, 21, 12), (19, 35, 14, -5), (20, 30, 16, -4), (16, 33, 18, 2), (16, 35, 17, 1), (16, 35, 17, 1), (18, 29, 18, 0), (21, 26, 17, -4), (12, 38, 20, 8), (14, 38, 18, 4), (20, 29, 16, -4), (16, 23, 23, 7), (14, 33, 20, 6), (19, 35, 14, -5), (24, 29, 12, -12), (13, 47, 14, 1), (21, 31, 14, -7), (18, 38, 14, -4), (16, 26, 22, 6), (20, 29, 16, -4), (18, 25, 20, 2), (22, 23, 17, -5), (21, 38, 11, -10), (24, 22, 16, -8), (19, 33, 15, -4), (17, 41, 13, -4), (13, 39, 18, 5), (18, 38, 14, -4), (17, 29, 19, 2), (21, 30, 15, -6), (12, 42, 18, 6), (13, 30, 23, 10), (17, 36, 16, -1), (14, 33, 20, 6), (15, 45, 13, -2), (15, 40, 16, 1), (18, 26, 20, 2), (16, 30, 20, 4), (13, 43, 16, 3), (20, 27, 17, -3), (14, 43, 15, 1), (13, 35, 20, 7), (25, 31, 10, -15), (17, 35, 16, -1), (19, 28, 18, -1), (20, 32, 15, -5), (14, 49, 12, -2), (14, 35, 19, 5), (14, 40, 17, 3), (17, 33, 17, 0), (20, 33, 14, -6), (20, 35, 13, -7), (19, 33, 15, -4), (16, 35, 17, 1), (16, 31, 19, 3), (21, 33, 13, -8), (18, 39, 13, -5), (12, 39, 19, 7), (25, 33, 9, -16), (17, 33, 17, 0), (13, 30, 23, 10), (15, 29, 21, 6), (11, 39, 20, 9), (15, 34, 19, 4), (17, 39, 14, -3), (20, 27, 17, -3), (21, 30, 15, -6), (15, 38, 17, 2), (18, 27, 19, 1), (17, 30, 19, 2), (19, 26, 19, 0), (19, 29, 17, -2), (14, 28, 23, 9), (15, 35, 18, 3), (14, 23, 25, 11), (18, 39, 13, -5), (15, 41, 15, 0), (19, 34, 15, -4), (16, 37, 16, 0), (10, 32, 25, 15), (16, 32, 19, 3), (15, 29, 21, 6), (21, 27, 16, -5), (23, 29, 13, -10), (22, 29, 14, -8), (22, 38, 10, -12), (18, 27, 19, 1), (13, 28, 24, 11), (19, 26, 19, 0), (19, 33, 15, -4), (19, 29, 17, -2), (19, 43, 10, -9), (20, 22, 20, 0), (22, 28, 15, -7), (19, 32, 16, -3), (17, 42, 13, -4), (16, 30, 20, 4), (19, 33, 15, -4), (19, 24, 20, 1), (16, 32, 19, 3), (16, 32, 19, 3), (13, 29, 23, 10), (15, 29, 21, 6), (14, 36, 19, 5), (19, 35, 14, -5), (20, 37, 12, -8), (19, 29, 17, -2), (16, 33, 18, 2), (19, 38, 13, -6), (18, 39, 13, -5), (17, 34, 17, 0), (19, 38, 13, -6), (17, 29, 19, 2), (17, 38, 15, -2), (23, 26, 15, -8), (22, 31, 13, -9), (15, 31, 20, 5), (19, 33, 15, -4), (17, 29, 19, 2), (21, 29, 15, -6), (15, 28, 22, 7), (21, 29, 15, -6), (16, 28, 21, 5), (17, 31, 18, 1), (21, 31, 14, -7), (20, 28, 17, -3), (20, 33, 14, -6), (16, 37, 16, 0), (18, 31, 17, -1), (16, 39, 15, -1), (22, 33, 12, -10), (12, 37, 20, 8), (13, 31, 22, 9), (17, 38, 15, -2), (20, 30, 16, -4), (17, 39, 14, -3), (13, 37, 19, 6), (12, 33, 22, 10), (19, 31, 16, -3), (23, 37, 9, -14), (15, 45, 13, -2), (19, 35, 14, -5), (17, 50, 9, -8), (18, 25, 20, 2), (16, 43, 13, -3), (13, 37, 19, 6), (21, 31, 14, -7), (14, 35, 19, 5), (19, 27, 18, -1), (21, 41, 9, -12), (19, 37, 13, -6), (22, 33, 12, -10), (22, 32, 13, -9), (14, 31, 21, 7), (22, 26, 16, -6), (22, 29, 14, -8), (17, 37, 15, -2), (21, 35, 12, -9), (15, 39, 16, 1), (17, 32, 18, 1), (15, 46, 13, -2), (12, 43, 17, 5), (18, 43, 11, -7), (13, 43, 16, 3), (17, 30, 19, 2), (19, 35, 14, -5), (16, 41, 14, -2), (17, 39, 14, -3), (12, 31, 23, 11), (22, 26, 16, -6), (11, 43, 18, 7), (24, 37, 8, -16), (17, 36, 16, -1), (17, 39, 14, -3), (20, 33, 14, -6), (15, 37, 17, 2), (16, 46, 12, -4), (13, 33, 21, 8), (19, 40, 12, -7), (19, 27, 18, -1), (17, 40, 14, -3), (13, 37, 19, 6), (15, 39, 16, 1), (14, 39, 17, 3), (20, 32, 15, -5), (17, 35, 16, -1), (12, 41, 18, 6), (16, 36, 17, 1), (16, 21, 24, 8), (21, 33, 13, -8), (17, 23, 22, 5), (18, 39, 13, -5), (17, 43, 12, -5), (20, 31, 15, -5), (19, 43, 10, -9), (20, 34, 14, -6), (15, 32, 20, 5), (20, 30, 16, -4), (15, 39, 16, 1), (21, 37, 11, -10), (11, 39, 20, 9), (15, 39, 16, 1), (16, 31, 19, 3), (16, 37, 16, 0), (14, 27, 23, 9), (17, 35, 16, -1), (12, 41, 18, 6), (17, 41, 13, -4), (21, 31, 14, -7), (18, 29, 18, 0), (19, 35, 14, -5), (19, 27, 18, -1), (20, 41, 10, -10), (16, 35, 17, 1), (19, 35, 14, -5), (16, 27, 21, 5), (12, 30, 24, 12), (18, 34, 16, -2), (17, 38, 15, -2), (19, 25, 19, 0), (17, 27, 20, 3), (21, 35, 12, -9), (13, 37, 19, 6), (15, 35, 18, 3), (16, 42, 14, -2), (17, 32, 18, 1), (13, 38, 19, 6), (13, 39, 18, 5), (15, 33, 19, 4), (23, 31, 12, -11), (18, 37, 14, -4), (17, 31, 18, 1), (12, 36, 21, 9), (22, 39, 9, -13), (13, 48, 14, 1), (18, 31, 17, -1), (12, 35, 21, 9), (12, 41, 18, 6), (11, 39, 20, 9), (20, 27, 17, -3), (20, 31, 15, -5), (15, 43, 14, -1), (18, 39, 13, -5), (22, 29, 14, -8), (23, 31, 12, -11), (21, 32, 14, -7), (13, 31, 22, 9), (17, 33, 17, 0), (15, 31, 20, 5), (15, 35, 18, 3), (18, 31, 17, -1), (17, 33, 17, 0), (15, 38, 17, 2), (18, 31, 17, -1), (13, 41, 17, 4), (15, 40, 16, 1), (18, 25, 20, 2), (14, 31, 21, 7), (17, 38, 15, -2), (17, 31, 18, 1), (11, 39, 20, 9), (13, 33, 21, 8), (18, 38, 14, -4), (16, 31, 19, 3), (16, 31, 19, 3), (13, 32, 22, 9), (17, 28, 20, 3), (15, 39, 16, 1), (20, 28, 17, -3), (15, 34, 19, 4), (14, 31, 21, 7), (18, 31, 17, -1), (16, 31, 19, 3), (17, 35, 16, -1), (16, 34, 18, 2), (18, 35, 15, -3), (15, 37, 17, 2), (15, 27, 22, 7), (15, 33, 19, 4), (26, 26, 12, -14), (21, 25, 17, -4), (17, 40, 14, -3), (15, 38, 17, 2), (21, 25, 17, -4), (17, 27, 20, 3), (21, 37, 11, -10), (23, 33, 11, -12), (16, 29, 20, 4), (16, 29, 20, 4), (20, 34, 14, -6), (23, 24, 16, -7), (16, 38, 16, 0), (22, 29, 14, -8), (20, 29, 16, -4), (15, 27, 22, 7), (12, 35, 21, 9), (19, 39, 12, -7), (14, 35, 19, 5), (12, 45, 16, 4), (13, 33, 21, 8), (18, 37, 14, -4), (23, 26, 15, -8), (19, 32, 16, -3), (9, 35, 24, 15), (17, 29, 19, 2), (15, 34, 19, 4), (22, 31, 13, -9), (17, 40, 14, -3), (12, 35, 21, 9), (12, 31, 23, 11), (13, 45, 15, 2), (23, 25, 15, -8), (19, 40, 12, -7), (25, 31, 10, -15), (20, 31, 15, -5), (12, 39, 19, 7), (13, 35, 20, 7), (14, 40, 17, 3), (22, 23, 17, -5), (18, 30, 18, 0), (18, 32, 17, -1), (24, 36, 9, -15), (16, 28, 21, 5), (15, 38, 17, 2), (15, 28, 22, 7), (17, 34, 17, 0), (19, 23, 20, 1), (17, 37, 15, -2), (11, 34, 23, 12), (17, 31, 18, 1), (17, 35, 16, -1), (17, 38, 15, -2), (16, 31, 19, 3), (20, 31, 15, -5), (17, 25, 21, 4), (21, 33, 13, -8), (15, 38, 17, 2), (9, 34, 25, 16), (19, 32, 16, -3), (26, 31, 9, -17), (15, 39, 16, 1), (15, 36, 18, 3), (18, 36, 15, -3), (18, 27, 19, 1), (14, 33, 20, 6), (21, 27, 16, -5), (17, 35, 16, -1), (9, 31, 26, 17), (20, 32, 15, -5), (13, 33, 21, 8), (22, 25, 16, -6), (14, 47, 13, -1), (16, 35, 17, 1), (16, 36, 17, 1), (17, 35, 16, -1), (15, 29, 21, 6), (18, 28, 19, 1), (17, 33, 17, 0), (19, 34, 15, -4), (15, 35, 18, 3), (15, 28, 22, 7), (19, 29, 17, -2), (12, 33, 22, 10), (13, 37, 19, 6), (13, 35, 20, 7), (13, 29, 23, 10), (18, 38, 14, -4), (23, 36, 10, -13), (16, 27, 21, 5), (14, 35, 19, 5), (14, 35, 19, 5), (15, 31, 20, 5), (17, 34, 17, 0), (12, 38, 20, 8), (19, 35, 14, -5), (16, 33, 18, 2), (18, 35, 15, -3), (18, 38, 14, -4), (20, 43, 9, -11), (17, 32, 18, 1), (17, 34, 17, 0), (21, 37, 11, -10), (17, 33, 17, 0), (11, 35, 22, 11), (20, 29, 16, -4), (22, 25, 16, -6), (18, 31, 17, -1), (14, 39, 17, 3), (22, 23, 17, -5), (17, 32, 18, 1), (13, 37, 19, 6), (14, 29, 22, 8), (22, 35, 11, -11), (18, 34, 16, -2), (12, 43, 17, 5), (20, 21, 20, 0), (17, 37, 15, -2), (8, 47, 19, 11), (17, 34, 17, 0), (13, 44, 16, 3), (16, 40, 15, -1), (14, 33, 20, 6), (16, 39, 15, -1), (15, 29, 21, 6), (14, 35, 19, 5), (15, 28, 22, 7), (18, 34, 16, -2), (19, 34, 15, -4), (19, 36, 14, -5), (20, 35, 13, -7), (18, 32, 17, -1), (14, 48, 13, -1), (18, 31, 17, -1), (12, 31, 23, 11), (17, 27, 20, 3), (13, 29, 23, 10), (13, 43, 16, 3), (20, 33, 14, -6), (16, 33, 18, 2), (17, 28, 20, 3), (14, 41, 16, 2), (14, 39, 17, 3), (13, 29, 23, 10), (18, 27, 19, 1), (17, 31, 18, 1), (10, 41, 20, 10), (16, 43, 13, -3), (18, 29, 18, 0), (17, 35, 16, -1), (18, 35, 15, -3), (21, 27, 16, -5), (14, 33, 20, 6), (16, 26, 22, 6), (19, 32, 16, -3), (18, 25, 20, 2), (15, 33, 19, 4), (19, 24, 20, 1), (18, 31, 17, -1), (20, 36, 13, -7), (16, 35, 17, 1), (13, 31, 22, 9), (23, 27, 14, -9), (22, 25, 16, -6), (19, 37, 13, -6), (15, 30, 21, 6), (15, 43, 14, -1), (17, 39, 14, -3), (20, 32, 15, -5), (14, 33, 20, 6), (16, 35, 17, 1), (18, 34, 16, -2), (11, 37, 21, 10), (17, 41, 13, -4), (16, 44, 13, -3), (19, 35, 14, -5), (19, 19, 22, 3), (15, 37, 17, 2), (19, 33, 15, -4), (16, 35, 17, 1), (17, 35, 16, -1), (13, 38, 19, 6), (19, 44, 10, -9), (16, 26, 22, 6), (12, 32, 23, 11), (18, 37, 14, -4), (18, 41, 12, -6), (15, 38, 17, 2), (19, 27, 18, -1), (19, 43, 10, -9), (17, 25, 21, 4), (22, 23, 17, -5), (11, 42, 19, 8), (21, 32, 14, -7), (15, 39, 16, 1), (18, 36, 15, -3), (20, 41, 10, -10), (8, 44, 21, 13), (15, 35, 18, 3), (16, 36, 17, 1), (17, 37, 15, -2), (18, 30, 18, 0), (17, 38, 15, -2), (17, 37, 15, -2), (19, 33, 15, -4), (15, 39, 16, 1), (17, 33, 17, 0), (13, 27, 24, 11), (18, 33, 16, -2), (16, 33, 18, 2), (11, 43, 18, 7), (21, 23, 18, -3), (17, 33, 17, 0), (18, 28, 19, 1), (25, 25, 13, -12), (11, 41, 19, 8), (23, 28, 14, -9), (13, 40, 18, 5), (17, 35, 16, -1), (17, 35, 16, -1), (19, 31, 16, -3), (16, 36, 17, 1), (20, 35, 13, -7), (17, 44, 12, -5), (19, 32, 16, -3), (16, 33, 18, 2), (11, 37, 21, 10), (14, 31, 21, 7), (16, 32, 19, 3), (13, 39, 18, 5), (22, 27, 15, -7), (15, 41, 15, 0), (20, 39, 11, -9), (17, 38, 15, -2), (20, 22, 20, 0), (21, 28, 16, -5), (14, 31, 21, 7), (17, 35, 16, -1), (16, 32, 19, 3), (18, 30, 18, 0), (14, 37, 18, 4), (15, 29, 21, 6), (20, 40, 11, -9), (16, 33, 18, 2), (18, 35, 15, -3), (14, 40, 17, 3), (16, 27, 21, 5), (20, 28, 17, -3), (15, 33, 19, 4), (12, 33, 22, 10), (14, 45, 14, 0), (20, 39, 11, -9), (17, 24, 22, 5), (13, 29, 23, 10), (16, 27, 21, 5), (22, 34, 12, -10), (14, 33, 20, 6), (18, 31, 17, -1), (19, 31, 16, -3), (17, 46, 11, -6), (14, 43, 15, 1), (19, 33, 15, -4), (17, 37, 15, -2), (20, 28, 17, -3), (15, 36, 18, 3), (19, 37, 13, -6), (21, 38, 11, -10), (21, 37, 11, -10), (19, 36, 14, -5), (16, 39, 15, -1), (16, 29, 20, 4), (20, 26, 18, -2), (17, 39, 14, -3), (16, 27, 21, 5), (16, 34, 18, 2), (15, 45, 13, -2), (21, 25, 17, -4), (20, 27, 17, -3), (11, 42, 19, 8), (19, 27, 18, -1), (22, 34, 12, -10), (10, 40, 21, 11), (22, 26, 16, -6), (21, 29, 15, -6), (6, 37, 26, 20), (14, 35, 19, 5), (17, 33, 17, 0), (18, 38, 14, -4), (16, 33, 18, 2), (18, 33, 16, -2), (16, 35, 17, 1), (16, 40, 15, -1), (16, 35, 17, 1), (12, 37, 20, 8), (19, 30, 17, -2), (15, 47, 12, -3), (20, 27, 17, -3), (17, 39, 14, -3), (14, 45, 14, 0), (20, 38, 12, -8), (17, 48, 10, -7), (13, 35, 20, 7), (16, 25, 22, 6), (25, 19, 16, -9), (20, 39, 11, -9), (15, 41, 15, 0), (20, 31, 15, -5), (19, 27, 18, -1), (8, 45, 20, 12), (18, 35, 15, -3), (18, 22, 22, 4), (13, 39, 18, 5), (18, 38, 14, -4), (20, 20, 21, 1), (12, 45, 16, 4), (22, 28, 15, -7), (17, 38, 15, -2), (15, 43, 14, -1), (20, 26, 18, -2), (16, 35, 17, 1), (14, 37, 18, 4), (16, 32, 19, 3), (17, 36, 16, -1), (18, 30, 18, 0), (22, 28, 15, -7), (20, 26, 18, -2), (17, 30, 19, 2), (14, 39, 17, 3), (20, 35, 13, -7), (21, 33, 13, -8), (21, 27, 16, -5), (19, 35, 14, -5), (16, 41, 14, -2), (21, 23, 18, -3), (15, 39, 16, 1), (15, 38, 17, 2), (19, 29, 17, -2), (19, 36, 14, -5)]

@+

Dernière modification par yoshi (09-11-2014 21:36:38)

Bemo52 · 09-11-2014 21:55:45

Merci beaucoup.
Je viens de verifier quelques triplets et cela ne donne pas 100 lancers.
Exemple :
(14,18,23)

14 (10) et 23 (11) prennent 2 lancers soit 37*2=74
74+18 devrait donner 100 ou au moins 99
74+18=92
(17,22,23)
dnne 102

Je ne sais pas comment tu as procede mais il y a une erreur quelque part dans le programme.

Merci de reverifier

yoshi · 10-11-2014 10:23:17

Salut,

Exact..
Je n'ai pas trouvé pourquoi rapidement, alors j'ai tout reprogrammé : cette fois, ça m'a l'air correct (j'ai inclus un "mouchard").
Mais cela signifie que c'est faux depuis le début.
Donc, voilà 1000 essais de ta demande d'origine :
[(56, 14), (47, 17), (45, 20), (56, 14), (58, 14), (49, 18), (52, 13), (56, 14), (56, 12), (45, 18), (57, 12), (55, 12), (48, 17), (47, 19), (60, 9), (50, 15), (46, 17), (47, 20), (45, 20), (50, 16), (47, 17), (53, 15), (49, 15), (50, 16), (54, 13), (56, 15), (54, 15), (51, 16), (55, 16), (45, 20), (45, 21), (52, 17), (41, 23), (52, 16), (55, 14), (51, 13), (58, 9), (49, 18), (49, 18), (50, 18), (45, 18), (46, 17), (43, 17), (47, 17), (51, 19), (48, 15), (53, 11), (52, 15), (52, 16), (54, 16), (46, 17), (52, 15), (42, 19), (55, 14), (41, 22), (46, 23), (59, 10), (45, 18), (58, 14), (54, 17), (43, 21), (57, 14), (48, 18), (49, 16), (50, 12), (39, 24), (50, 17), (52, 15), (50, 13), (45, 21), (38, 23), (52, 17), (55, 16), (47, 19), (51, 19), (52, 17), (49, 19), (53, 15), (43, 21), (43, 21), (48, 20), (54, 14), (52, 16), (52, 16), (60, 9), (51, 17), (53, 16), (62, 13), (49, 16), (54, 14), (46, 17), (64, 12), (52, 16), (45, 23), (50, 17), (46, 17), (63, 11), (58, 13), (51, 17), (47, 16), (58, 13), (52, 15), (43, 19), (50, 17), (42, 23), (47, 18), (51, 18), (48, 18), (48, 21), (48, 17), (53, 13), (47, 17), (51, 19), (52, 15), (51, 16), (48, 17), (49, 17), (42, 20), (55, 15), (51, 16), (48, 17), (59, 10), (50, 14), (48, 16), (45, 21), (45, 18), (53, 14), (44, 21), (55, 15), (54, 16), (41, 22), (45, 19), (59, 13), (52, 13), (46, 22), (48, 18), (57, 14), (47, 20), (56, 15), (49, 19), (47, 19), (41, 20), (41, 22), (43, 20), (54, 14), (61, 11), (48, 16), (55, 15), (53, 12), (57, 10), (41, 20), (44, 16), (53, 15), (52, 17), (54, 14), (47, 18), (48, 18), (52, 17), (45, 17), (44, 17), (51, 18), (49, 18), (47, 18), (49, 18), (50, 19), (51, 15), (52, 17), (47, 20), (54, 17), (50, 15), (56, 14), (46, 19), (57, 14), (49, 20), (61, 11), (41, 20), (46, 17), (52, 16), (45, 19), (56, 11), (47, 19), (54, 13), (42, 20), (50, 17), (56, 15), (45, 19), (52, 18), (47, 18), (45, 19), (46, 21), (45, 19), (51, 17), (48, 19), (51, 13), (54, 14), (52, 16), (45, 20), (52, 16), (58, 14), (47, 20), (52, 16), (50, 15), (56, 13), (56, 11), (58, 14), (55, 16), (45, 20), (49, 15), (48, 18), (51, 12), (51, 13), (52, 16), (55, 14), (46, 20), (44, 20), (49, 18), (49, 19), (48, 16), (43, 21), (55, 13), (55, 17), (45, 16), (51, 17), (53, 13), (54, 14), (49, 15), (50, 19), (51, 17), (45, 21), (53, 16), (40, 20), (46, 19), (38, 22), (61, 10), (50, 18), (47, 17), (53, 15), (58, 11), (57, 13), (52, 15), (52, 15), (59, 13), (50, 17), (45, 18), (49, 18), (50, 17), (54, 14), (53, 16), (53, 16), (47, 17), (46, 17), (52, 18), (55, 12), (44, 21), (57, 16), (43, 21), (43, 23), (45, 20), (53, 15), (57, 10), (55, 16), (44, 21), (52, 17), (48, 16), (41, 22), (55, 13), (47, 17), (55, 12), (52, 16), (39, 25), (55, 16), (42, 18), (44, 19), (49, 17), (46, 17), (52, 17), (51, 16), (53, 17), (55, 18), (41, 18), (54, 15), (43, 19), (39, 24), (46, 15), (39, 25), (53, 14), (51, 16), (47, 20), (52, 17), (54, 12), (50, 19), (49, 18), (52, 15), (50, 16), (57, 12), (43, 18), (62, 9), (49, 18), (41, 23), (50, 14), (44, 22), (47, 19), (58, 13), (44, 19), (56, 16), (55, 13), (51, 15), (51, 15), (47, 20), (58, 11), (47, 16), (51, 16), (53, 14), (45, 17), (50, 15), (57, 15), (50, 16), (50, 18), (53, 15), (47, 20), (51, 16), (51, 15), (56, 13), (49, 17), (49, 15), (58, 12), (47, 18), (59, 14), (66, 8), (54, 14), (51, 15), (49, 14), (46, 20), (50, 19), (50, 12), (44, 22), (47, 17), (51, 18), (47, 15), (56, 9), (52, 15), (46, 18), (53, 12), (45, 19), (53, 13), (48, 17), (49, 16), (53, 14), (61, 11), (52, 17), (49, 20), (61, 10), (53, 16), (49, 20), (50, 18), (51, 15), (45, 18), (51, 13), (57, 13), (54, 17), (47, 20), (54, 16), (58, 10), (44, 20), (56, 11), (57, 14), (50, 16), (51, 15), (48, 20), (54, 16), (47, 15), (52, 17), (41, 22), (52, 14), (44, 20), (47, 20), (60, 13), (54, 12), (58, 12), (51, 13), (52, 19), (49, 17), (45, 19), (49, 19), (48, 19), (56, 12), (55, 15), (46, 21), (58, 10), (53, 13), (46, 20), (53, 17), (46, 20), (50, 18), (58, 12), (51, 19), (55, 14), (50, 17), (52, 13), (56, 12), (47, 17), (45, 19), (46, 20), (49, 19), (59, 11), (49, 20), (41, 21), (46, 17), (48, 15), (55, 12), (51, 16), (44, 20), (56, 12), (57, 13), (53, 14), (53, 16), (48, 22), (54, 11), (52, 17), (47, 19), (54, 12), (49, 17), (51, 15), (44, 19), (50, 14), (46, 17), (38, 24), (60, 11), (48, 17), (56, 13), (46, 17), (52, 18), (52, 16), (53, 13), (49, 17), (49, 18), (45, 16), (56, 15), (47, 16), (51, 14), (47, 18), (53, 14), (53, 15), (54, 13), (48, 19), (49, 19), (50, 17), (55, 15), (47, 20), (45, 21), (54, 13), (53, 16), (57, 13), (53, 14), (46, 21), (57, 13), (51, 15), (53, 17), (55, 16), (57, 13), (47, 16), (53, 16), (51, 17), (49, 17), (57, 13), (50, 14), (53, 14), (46, 20), (52, 17), (53, 15), (46, 20), (49, 17), (47, 19), (56, 10), (50, 18), (47, 16), (43, 20), (43, 21), (50, 17), (61, 10), (51, 17), (56, 13), (53, 17), (53, 13), (46, 18), (50, 17), (58, 14), (58, 13), (50, 17), (45, 19), (48, 17), (55, 13), (55, 15), (58, 12), (44, 21), (49, 19), (53, 15), (42, 23), (45, 20), (48, 17), (47, 18), (36, 25), (51, 16), (49, 19), (47, 21), (39, 23), (59, 14), (44, 20), (51, 14), (62, 11), (49, 18), (53, 14), (57, 11), (57, 12), (44, 21), (50, 18), (51, 15), (57, 14), (58, 10), (56, 15), (65, 11), (38, 24), (49, 20), (53, 16), (49, 17), (59, 12), (44, 19), (41, 21), (56, 13), (56, 15), (50, 17), (53, 16), (45, 19), (61, 8), (51, 17), (52, 13), (48, 16), (59, 10), (48, 13), (51, 13), (47, 21), (39, 24), (60, 10), (48, 17), (46, 19), (56, 16), (43, 21), (54, 14), (43, 22), (51, 15), (55, 13), (52, 17), (52, 16), (53, 14), (48, 17), (46, 21), (47, 21), (49, 16), (49, 17), (47, 16), (53, 13), (55, 13), (47, 16), (50, 19), (49, 16), (51, 17), (52, 16), (55, 12), (41, 21), (58, 13), (60, 12), (54, 14), (58, 10), (45, 20), (44, 20), (45, 18), (43, 22), (47, 16), (47, 18), (53, 15), (45, 20), (48, 15), (49, 16), (49, 19), (53, 16), (54, 13), (47, 20), (47, 17), (48, 19), (43, 20), (46, 17), (51, 14), (53, 17), (49, 16), (55, 15), (59, 10), (59, 12), (56, 14), (44, 23), (51, 15), (48, 19), (55, 13), (47, 18), (57, 13), (49, 17), (45, 20), (43, 20), (56, 14), (44, 20), (52, 14), (45, 17), (38, 23), (49, 17), (51, 17), (61, 11), (58, 10), (49, 18), (51, 17), (57, 13), (49, 16), (49, 15), (56, 13), (47, 19), (45, 19), (61, 10), (48, 17), (51, 17), (48, 17), (45, 19), (55, 16), (64, 11), (54, 18), (50, 16), (52, 15), (48, 20), (48, 17), (52, 15), (56, 13), (44, 20), (46, 20), (58, 11), (52, 16), (46, 18), (51, 13), (47, 17), (48, 19), (48, 15), (42, 23), (43, 23), (52, 15), (47, 17), (51, 16), (56, 15), (52, 16), (55, 12), (50, 15), (45, 19), (50, 19), (42, 23), (49, 17), (51, 17), (42, 22), (50, 18), (46, 18), (56, 11), (47, 17), (33, 27), (46, 18), (46, 17), (57, 13), (51, 12), (44, 22), (50, 17), (51, 15), (41, 20), (48, 17), (42, 20), (41, 22), (48, 21), (45, 18), (45, 22), (41, 21), (48, 18), (57, 12), (52, 17), (52, 14), (53, 16), (57, 12), (54, 15), (47, 15), (44, 18), (47, 14), (45, 18), (54, 14), (49, 18), (47, 15), (47, 19), (59, 13), (50, 18), (45, 19), (49, 17), (52, 14), (41, 25), (58, 12), (47, 17), (38, 25), (49, 17), (58, 11), (53, 13), (46, 20), (48, 17), (56, 13), (47, 13), (50, 17), (55, 15), (47, 17), (45, 22), (55, 13), (50, 19), (47, 15), (58, 12), (48, 16), (52, 17), (54, 12), (52, 14), (49, 18), (54, 13), (48, 18), (51, 16), (45, 19), (54, 14), (54, 12), (39, 24), (53, 16), (51, 16), (48, 17), (52, 16), (56, 15), (50, 17), (44, 16), (54, 14), (47, 17), (45, 21), (45, 19), (59, 13), (47, 19), (53, 15), (50, 18), (61, 8), (52, 16), (52, 17), (50, 16), (50, 17), (57, 13), (50, 18), (44, 18), (50, 17), (50, 16), (55, 15), (53, 17), (53, 14), (50, 16), (37, 25), (53, 17), (55, 15), (38, 22), (54, 14), (56, 13), (44, 21), (47, 17), (53, 14), (41, 23), (46, 17), (44, 21), (52, 14), (41, 21), (52, 16), (47, 19), (61, 10), (49, 16), (46, 18), (46, 21), (47, 16), (52, 19), (55, 12), (48, 17), (45, 20), (49, 18), (54, 14), (46, 19), (46, 19), (37, 24), (51, 18), (54, 16), (56, 13), (45, 21), (49, 17), (54, 13), (47, 19), (38, 23), (55, 14), (54, 12), (48, 15), (44, 19), (53, 14), (55, 14), (58, 11), (60, 13), (56, 14), (56, 12), (52, 15), (45, 21), (45, 17), (51, 19), (55, 13), (54, 13), (54, 15), (41, 21), (44, 18), (47, 18), (61, 13), (60, 12), (56, 13), (46, 19), (44, 17), (53, 13), (45, 20), (51, 13), (42, 20), (52, 13), (45, 18), (45, 18), (49, 15), (52, 16), (50, 20), (51, 14), (60, 13), (46, 20), (39, 24), (50, 18), (65, 10), (48, 17), (51, 17), (57, 11), (46, 18), (49, 18), (46, 16), (54, 15), (46, 19), (59, 14), (49, 18), (40, 21), (47, 18), (55, 12), (52, 15), (58, 11), (55, 16), (54, 16), (51, 20), (44, 21), (52, 15), (56, 12), (51, 17), (59, 10), (47, 19), (48, 18), (56, 12), (52, 18), (54, 14), (49, 14), (57, 16), (51, 15), (54, 16), (53, 12), (47, 18), (42, 24), (52, 14), (47, 20), (45, 17), (44, 19), (46, 20), (50, 16), (47, 17), (52, 13), (50, 19), (55, 15), (56, 14), (51, 16), (48, 18), (53, 12), (50, 15), (53, 15), (49, 18), (55, 16), (48, 18), (52, 14), (60, 11), (47, 17), (46, 16), (49, 17), (54, 14), (48, 17), (54, 15), (51, 17), (45, 18), (53, 13), (56, 13), (50, 17), (51, 14), (55, 15), (53, 16), (56, 17), (45, 21), (53, 13), (54, 15), (57, 14), (50, 17), (53, 15), (51, 16), (53, 15), (53, 15), (49, 16), (53, 13), (51, 17), (52, 15), (54, 12), (56, 15), (50, 16), (49, 17), (49, 17), (57, 13), (49, 15), (52, 13), (47, 20), (49, 16), (49, 16), (57, 10), (48, 18), (46, 17), (50, 18), (51, 16), (45, 22), (53, 15), (48, 16), (58, 12), (48, 18), (52, 19), (60, 10), (53, 15), (53, 14), (52, 15), (44, 20), (48, 18), (46, 21), (54, 14), (44, 19), (45, 19), (49, 18), (61, 12), (57, 13), (50, 17), (53, 16), (63, 10), (56, 15), (47, 18), (53, 14), (49, 16), (59, 11), (52, 18), (46, 18), (43, 21), (42, 22), (48, 19), (50, 15), (44, 20), (49, 17), (54, 14), (52, 17), (50, 17), (49, 17), (53, 14), (37, 23), (50, 14), (42, 21), (52, 15), (53, 15), (49, 17), (50, 16), (54, 13), (51, 17), (54, 15), (53, 15), (55, 15), (52, 17), (56, 13), (51, 15), (52, 14), (48, 18), (53, 13), (47, 18)]

Et 2000 autres avec la variante -1 :
[(13, 44, 15, 2), (13, 30, 22, 9), (17, 28, 19, 2), (13, 30, 22, 9), (16, 30, 19, 3), (14, 38, 17, 3), (24, 27, 12, -12), (16, 28, 20, 4), (14, 39, 16, 2), (22, 33, 11, -11), (19, 30, 16, -3), (13, 33, 20, 7), (14, 40, 16, 2), (14, 36, 18, 4), (15, 39, 15, 0), (19, 36, 13, -6), (21, 34, 12, -9), (12, 38, 19, 7), (21, 30, 14, -7), (17, 32, 17, 0), (14, 46, 13, -1), (16, 28, 20, 4), (18, 40, 12, -6), (17, 34, 16, -1), (19, 34, 14, -5), (17, 38, 14, -3), (14, 47, 12, -2), (18, 38, 13, -5), (18, 32, 16, -2), (14, 34, 19, 5), (14, 36, 18, 4), (18, 34, 15, -3), (19, 32, 15, -4), (14, 37, 17, 3), (23, 22, 16, -7), (10, 44, 18, 8), (19, 24, 19, 0), (18, 29, 17, -1), (12, 32, 22, 10), (15, 33, 18, 3), (12, 31, 22, 10), (24, 29, 11, -13), (10, 52, 14, 4), (13, 40, 17, 4), (16, 36, 16, 0), (15, 28, 21, 6), (18, 36, 14, -4), (19, 25, 18, -1), (20, 31, 14, -6), (17, 33, 16, -1), (16, 33, 17, 1), (11, 39, 19, 8), (17, 38, 14, -3), (16, 39, 14, -2), (17, 24, 21, 4), (17, 34, 16, -1), (25, 18, 16, 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(22, 32, 12, -10), (16, 36, 16, 0), (19, 28, 17, -2), (14, 40, 16, 2), (17, 36, 15, -2), (8, 44, 20, 12), (21, 39, 9, -12), (15, 40, 15, 0), (19, 36, 13, -6), (13, 36, 19, 6), (18, 33, 15, -3), (17, 24, 21, 4), (17, 25, 20, 3), (13, 40, 17, 4), (11, 35, 21, 10), (14, 36, 18, 4), (17, 36, 15, -2), (12, 33, 21, 9), (22, 34, 11, -11), (17, 29, 18, 1), (18, 40, 12, -6), (26, 34, 7, -19), (21, 23, 17, -4), (16, 25, 21, 5), (19, 23, 19, 0), (16, 33, 17, 1), (18, 38, 13, -5), (16, 36, 16, 0), (22, 22, 17, -5), (13, 27, 23, 10), (21, 26, 16, -5), (18, 33, 15, -3), (10, 34, 23, 13), (15, 40, 15, 0), (19, 35, 13, -6), (19, 36, 13, -6), (15, 24, 23, 8), (24, 34, 9, -15), (22, 32, 12, -10), (14, 34, 19, 5), (23, 28, 13, -10), (15, 36, 17, 2), (20, 31, 14, -6), (14, 31, 20, 6), (10, 38, 21, 11), (17, 35, 15, -2), (16, 36, 16, 0), (14, 40, 16, 2), (14, 31, 20, 6), (15, 36, 17, 2), (17, 35, 15, -2), (11, 38, 20, 9), (19, 28, 17, -2), (25, 26, 12, -13), (18, 28, 18, 0), (14, 38, 17, 3), (21, 33, 12, -9), (16, 38, 15, -1), (12, 35, 20, 8), (14, 32, 20, 6), (19, 36, 13, -6), (17, 34, 16, -1), (13, 34, 20, 7), (15, 35, 17, 2), (12, 34, 21, 9), (17, 32, 17, 0), (15, 42, 14, -1), (21, 37, 10, -11), (18, 32, 16, -2), (15, 33, 18, 3), (17, 38, 14, -3), (13, 42, 16, 3), (16, 36, 16, 0), (17, 32, 17, 0), (16, 40, 14, -2), (15, 36, 17, 2), (20, 31, 14, -6), (15, 34, 18, 3), (17, 33, 16, -1), (14, 40, 16, 2), (20, 32, 14, -6), (18, 40, 12, -6), (22, 38, 9, -13), (19, 28, 17, -2), (21, 34, 12, -9), (15, 31, 19, 4), (16, 23, 22, 6), (13, 28, 23, 10), (21, 34, 12, -9), (14, 28, 22, 8), (13, 36, 19, 6), (17, 31, 17, 0), (18, 37, 13, -5), (18, 31, 16, -2), (15, 31, 19, 4), (12, 42, 17, 5), (14, 28, 22, 8), (22, 34, 11, -11), (15, 32, 19, 4), (13, 38, 18, 5), (21, 32, 13, -8), (14, 43, 14, 0), (18, 35, 14, -4), (11, 40, 19, 8), (19, 22, 20, 1), (19, 28, 17, -2), (22, 25, 15, -7), (20, 23, 18, -2), (14, 42, 15, 1), (17, 43, 11, -6), (17, 30, 18, 1), (16, 29, 19, 3), (12, 34, 21, 9), (14, 38, 17, 3), (22, 29, 13, -9), (20, 28, 16, -4), (17, 38, 14, -3), (13, 34, 20, 7), (10, 41, 19, 9), (16, 41, 13, -3), (18, 38, 13, -5), (16, 34, 17, 1), (19, 41, 10, -9), (9, 36, 23, 14), (15, 30, 20, 5), (14, 33, 19, 5), (14, 34, 19, 5), (16, 39, 14, -2), (17, 33, 16, -1), (12, 32, 22, 10), (11, 32, 23, 12), (18, 20, 22, 4), (22, 35, 10, -12), (15, 41, 14, -1), (15, 32, 19, 4), (22, 24, 16, -6), (15, 26, 22, 7), (14, 38, 17, 3), (18, 29, 17, -1), (14, 37, 17, 3), (16, 30, 19, 3), (18, 33, 15, -3), (13, 32, 21, 8), (17, 24, 21, 4), (12, 39, 18, 6), (15, 33, 18, 3), (17, 29, 18, 1), (9, 36, 23, 14), (21, 22, 18, -3), (16, 37, 15, -1), (21, 26, 16, -5), (19, 34, 14, -5), (17, 38, 14, -3), (21, 32, 13, -8), (16, 37, 15, -1), (13, 33, 20, 7), (16, 40, 14, -2), (21, 30, 14, -7), (14, 32, 20, 6), (19, 28, 17, -2), (18, 26, 19, 1), (18, 25, 19, 1), (17, 28, 19, 2), (20, 39, 10, -10), (23, 34, 10, -13), (18, 28, 18, 0), (21, 33, 12, -9), (25, 25, 12, -13), (22, 23, 16, -6), (15, 35, 17, 2), (16, 28, 20, 4), (19, 26, 18, -1), (16, 31, 18, 2), (17, 38, 14, -3), (15, 32, 19, 4), (14, 39, 16, 2), (21, 43, 7, -14), (18, 32, 16, -2), (12, 28, 24, 12), (19, 32, 15, -4), (16, 41, 13, -3), (17, 35, 15, -2), (20, 27, 16, -4), (18, 30, 17, -1), (20, 32, 14, -6), (11, 37, 20, 9), (18, 33, 15, -3), (21, 30, 14, -7), (13, 40, 17, 4), (12, 30, 23, 11), (19, 35, 13, -6), (18, 32, 16, -2), (15, 29, 20, 5), (24, 31, 10, -14), (22, 32, 12, -10), (17, 39, 13, -4), (19, 32, 15, -4), (13, 40, 17, 4), (16, 36, 16, 0), (22, 32, 12, -10), (22, 31, 12, -10), (16, 40, 14, -2), (21, 30, 14, -7), (12, 36, 20, 8), (15, 33, 18, 3), (20, 36, 12, -8), (16, 37, 15, -1), (18, 37, 13, -5), (19, 31, 15, -4), (21, 29, 14, -7), (16, 30, 19, 3), (22, 23, 16, -6), (15, 34, 18, 3), (15, 36, 17, 2), (17, 28, 19, 2), (13, 36, 19, 6), (10, 29, 25, 15), (15, 37, 16, 1), (19, 32, 15, -4), (19, 26, 18, -1), (12, 38, 19, 7), (16, 25, 21, 5), (17, 29, 18, 1), (18, 40, 12, -6), (14, 40, 16, 2), (17, 40, 13, -4), (15, 33, 18, 3), (18, 30, 17, -1), (13, 30, 22, 9), (17, 32, 17, 0), (12, 40, 18, 6), (12, 33, 21, 9), (12, 40, 18, 6), (19, 28, 17, -2), (15, 33, 18, 3), (14, 38, 17, 3), (17, 32, 17, 0), (19, 26, 18, -1), (15, 50, 10, -5), (23, 30, 12, -11), (16, 32, 18, 2), (19, 32, 15, -4), (22, 38, 9, -13), (19, 26, 18, -1), (16, 29, 19, 3), (15, 41, 14, -1), (17, 38, 14, -3), (18, 35, 14, -4), (20, 28, 16, -4), (19, 30, 16, -3), (17, 34, 16, -1), (19, 35, 13, -6), (22, 28, 14, -8), (19, 36, 13, -6), (15, 34, 18, 3), (16, 37, 15, -1), (13, 42, 16, 3), (18, 33, 15, -3), (14, 40, 16, 2), (18, 28, 18, 0), (18, 34, 15, -3), (19, 32, 15, -4), (16, 40, 14, -2), (17, 46, 10, -7), (11, 41, 18, 7), (18, 43, 10, -8), (15, 36, 17, 2), (20, 32, 14, -6), (23, 25, 14, -9), (16, 38, 15, -1), (18, 30, 17, -1), (17, 34, 16, -1), (17, 24, 21, 4), (14, 42, 15, 1), (20, 33, 13, -7), (19, 33, 14, -5), (16, 34, 17, 1), (12, 36, 20, 8), (15, 41, 14, -1), (13, 34, 20, 7), (13, 32, 21, 8), (19, 31, 15, -4), (15, 38, 16, 1), (15, 44, 13, -2), (22, 33, 11, -11), (19, 26, 18, -1), (14, 34, 19, 5), (18, 36, 14, -4), (18, 30, 17, -1), (17, 31, 17, 0), (16, 22, 23, 7), (17, 30, 18, 1), (16, 34, 17, 1), (14, 32, 20, 6), (8, 33, 25, 17), (17, 30, 18, 1), (11, 34, 22, 11), (16, 44, 12, -4), (17, 32, 17, 0), (18, 31, 16, -2), (17, 34, 16, -1), (22, 34, 11, -11), (25, 28, 11, -14), (19, 32, 15, -4), (15, 44, 13, -2), (17, 34, 16, -1), (14, 38, 17, 3), (18, 28, 18, 0), (14, 40, 16, 2), (17, 42, 12, -5), (20, 32, 14, -6), (15, 30, 20, 5), (11, 44, 17, 6), (18, 30, 17, -1), (20, 32, 14, -6), (12, 33, 21, 9), (16, 32, 18, 2), (17, 36, 15, -2), (13, 37, 18, 5), (18, 25, 19, 1), (14, 27, 22, 8), (11, 32, 23, 12), (14, 40, 16, 2), (16, 32, 18, 2), (16, 39, 14, -2), (21, 34, 12, -9), (12, 32, 22, 10), (18, 18, 23, 5), (15, 35, 17, 2), (11, 40, 19, 8), (18, 28, 18, 0), (16, 40, 14, -2), (19, 36, 13, -6), (17, 32, 17, 0), (11, 35, 21, 10), (14, 37, 17, 3), (18, 24, 20, 2), (16, 42, 13, -3), (19, 33, 14, -5), (15, 26, 22, 7), (20, 35, 12, -8), (19, 29, 16, -3), (16, 28, 20, 4), (17, 35, 15, -2), (24, 31, 10, -14), (17, 42, 12, -5), (18, 35, 14, -4), (16, 34, 17, 1), (12, 39, 18, 6), (14, 37, 17, 3), (17, 28, 19, 2), (13, 36, 19, 6), (13, 48, 13, 0), (19, 36, 13, -6), (14, 40, 16, 2), (16, 34, 17, 1), (18, 40, 12, -6), (21, 31, 13, -8), (18, 34, 15, -3), (18, 35, 14, -4), (16, 38, 15, -1), (13, 35, 19, 6), (16, 28, 20, 4), (19, 23, 19, 0), (15, 28, 21, 6), (20, 29, 15, -5), (16, 37, 15, -1), (18, 37, 13, -5), (21, 30, 14, -7), (20, 22, 19, -1), (16, 30, 19, 3), (15, 36, 17, 2), (11, 44, 17, 6), (16, 38, 15, -1), (19, 25, 18, -1), (10, 38, 21, 11), (13, 43, 15, 2), (13, 31, 21, 8), (19, 37, 12, -7), (19, 28, 17, -2), (18, 36, 14, -4), (14, 31, 20, 6), (18, 36, 14, -4), (20, 38, 11, -9), (13, 38, 18, 5), (16, 26, 21, 5), (16, 38, 15, -1), (16, 30, 19, 3), (20, 24, 18, -2), (17, 34, 16, -1), (18, 40, 12, -6), (15, 47, 11, -4), (12, 41, 17, 5), (17, 29, 18, 1), (21, 28, 15, -6), (14, 40, 16, 2), (20, 24, 18, -2), (18, 20, 22, 4), (17, 31, 17, 0), (15, 28, 21, 6), (16, 36, 16, 0), (21, 35, 11, -10), (20, 30, 15, -5), (16, 34, 17, 1), (16, 30, 19, 3), (20, 26, 17, -3), (12, 37, 19, 7), (15, 25, 22, 7), (16, 42, 13, -3), (15, 42, 14, -1), (15, 37, 16, 1), (18, 30, 17, -1), (18, 34, 15, -3), (15, 30, 20, 5), (17, 43, 11, -6), (19, 29, 16, -3), (15, 40, 15, 0), (20, 32, 14, -6), (20, 26, 17, -3), (16, 31, 18, 2), (19, 33, 14, -5), (15, 34, 18, 3), (13, 32, 21, 8), (15, 37, 16, 1), (20, 40, 10, -10), (20, 32, 14, -6), (18, 25, 19, 1), (13, 42, 16, 3), (12, 38, 19, 7), (14, 28, 22, 8)]

@+

Bemo52 · 10-11-2014 13:35:56

Merci pour les rectifs.
Voila en fait mon probleme.
Il s`agit de jeux de hasard en general.
L`idee est de trouver une methode de jeu qui reduit sensiblement l`alea.
Ce n`est pas parfait. On voit les profits et pertes a travers la fonction sommatoire ( 4eme element + ou -).
Apres 100 lancers, le parieur a virtuellement gagne ou perdu. La mise est constante. Le gain est de 1 euro. Tu mises un euro, si tu gagnes tu as 2 euros gain soit un euro de benefice. Si tu perds, tu perds un euro.
La on parle d`un seul joueur.
Moi, je cherche une coordination de plusieurs methodes de jeu donc de plusieurs joueurs telle que le gain global des joueurs soit positif quelque soient les aleas. Le hasard n`est jamais aberrant, il est toujours "raisonnable".
Mon but n`est pas de gagner de l`argent mais de trouver une faille quelque part.
J`en ai deja trouvee quelques-unes mais vous n`allez pas me croire bien sur.
Merci.

Bemo52 · 10-11-2014 14:25:46

Pour etre plus precis le modele analyse correspond a un joueur qui parie de la maiere suivante :
Il vient pour parier.
Au premier lancer, il ne joue pas.
Il observe.
Si le 0 est affiche (pair par exemple pour la roulette), il ne joue pas.
Si le 1 est affiche, il mise un euro sur le 1 au prochain coup. S`il gagne il a un euro de benef s`il perd il perd un euro.
Il continue a jouer en appliquant la meme methode.
Dans les 2000 essais simules plus haut il est GLOBALEMENT gagnant (verifiez les calculs).
Bref, le gros des gains et pertes se situent entre +9 et -9.
Sans aller dans le detail, imaginons un certain nombre de joueurs "k". Les k joueurs sont parier simultanement sur plusieurs roulettes. A un moment dertermine, leur profit global sera NECESSAIREMENT positif. Si ces joueurs peuvent coordonner en temps reel la connaissance de leur profit global. Ils peuvent arreter de jouer leur objectif etant atteint.
Quel est le nombre de joueurs k optimal?
Je n`ai parle que d`une methode or il y en a d`autres plus efficaces peut etre.
Je n`ai pas fini d`ailleurs.

yoshi · 10-11-2014 15:55:53

Salut,

Tiens, alors voilà 2000 essais consécutifs de 100 lancers :
[(15, 24, 23, 8), (20, 29, 15, -5), (15, 40, 15, 0), (23, 28, 13, -10), (19, 20, 21, 2), (17, 36, 15, -2), (17, 39, 13, -4), (8, 46, 19, 11), (17, 37, 14, -3), (16, 32, 18, 2), (13, 36, 19, 6), (12, 43, 16, 4), (14, 39, 16, 2), (14, 31, 20, 6), (18, 35, 14, -4), (21, 34, 12, -9), (21, 26, 16, -5), (15, 30, 20, 5), (13, 34, 20, 7), (13, 39, 17, 4), (15, 30, 20, 5), (18, 30, 17, -1), (18, 32, 16, -2), (14, 31, 20, 6), (13, 34, 20, 7), (15, 36, 17, 2), (17, 28, 19, 2), (19, 37, 12, -7), (17, 25, 20, 3), (11, 49, 14, 3), (15, 37, 16, 1), (16, 38, 15, -1), (24, 33, 9, -15), (15, 34, 18, 3), (15, 28, 21, 6), (20, 26, 17, -3), (17, 32, 17, 0), (15, 31, 19, 4), (18, 47, 8, -10), (14, 34, 19, 5), (19, 37, 12, -7), (15, 25, 22, 7), (14, 39, 16, 2), (18, 28, 18, 0), (18, 38, 13, -5), (15, 32, 19, 4), (20, 22, 19, -1), (18, 35, 14, -4), (20, 27, 16, -4), (19, 24, 19, 0), (9, 38, 22, 13), (12, 30, 23, 11), (13, 39, 17, 4), (17, 31, 17, 0), (16, 40, 14, -2), (18, 26, 19, 1), (23, 36, 9, -14), (14, 22, 25, 11), (13, 31, 21, 8), (16, 40, 14, -2), (19, 34, 14, -5), (19, 28, 17, -2), (15, 40, 15, 0), (17, 35, 15, -2), (20, 32, 14, -6), (19, 26, 18, -1), (18, 34, 15, -3), (16, 28, 20, 4), (11, 33, 22, 11), (18, 28, 18, 0), (18, 25, 19, 1), (18, 36, 14, -4), (14, 35, 18, 4), (23, 28, 13, -10), (21, 31, 13, -8), (18, 38, 13, -5), (13, 46, 14, 1), (18, 39, 12, -6), (16, 32, 18, 2), (13, 41, 16, 3), (10, 42, 19, 9), (19, 30, 16, -3), (17, 32, 17, 0), (17, 33, 16, -1), (12, 38, 19, 7), (22, 34, 11, -11), (22, 36, 10, -12), (16, 36, 16, 0), (16, 48, 10, -6), (17, 35, 15, -2), (12, 40, 18, 6), (15, 35, 17, 2), (14, 33, 19, 5), (12, 30, 23, 11), (21, 29, 14, -7), (16, 40, 14, -2), (15, 32, 19, 4), (12, 35, 20, 8), (16, 34, 17, 1), (17, 34, 16, -1), (14, 37, 17, 3), (20, 34, 13, -7), (13, 36, 19, 6), (20, 26, 17, -3), (16, 32, 18, 2), (16, 30, 19, 3), (15, 29, 20, 5), (19, 27, 17, -2), (16, 42, 13, -3), (21, 31, 13, -8), (17, 36, 15, -2), (18, 44, 10, -8), (18, 34, 15, -3), (14, 26, 23, 9), 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21, 6), (15, 32, 19, 4), (13, 42, 16, 3), (18, 34, 15, -3), (22, 30, 13, -9), (18, 30, 17, -1)]

Y a un autre gars avant toi qui cherchait des trucs pour les tirages...
Va voir là :
http://www.bibmath.net/forums/viewtopic.php?id=6736
10000 c'est possible, sans pb, mais résultats par mail dans fichier .odt ou .pdf...

@+

Bemo52 · 10-11-2014 16:19:23

Merci pour l`info sauf que son probleme est different du mien.
Je m`explique :
Le hasard est ce qu`il est.
Je ne cherche pas a predire.
Imaginons qu`il existe un certain nombre de methodes de jeu.
Notons leur nombre k.
Imaginons que l`ensemble de ces methodes independantes couvre tout le champ des possibles.
Chacune de ces methodes va realiser des gains ou des pertes a un instant t.
Si on arrive a trouver un instant t tel que ces k methodes puissent GLOBALEMENT degager un profit avec une probabilite de 100% on brise le systeme.
Est-ce possible?
Je dis oui meme si pour l`instant j`ai du mal a le prouver.
Meme jeu avec 2 joueurs :
Le joueur 1 mise un euro a l`instant t quand le 1 s`affiche au lancer t-1. Il ne mise rien a l`instant t quand le 0 s`affiche a l`instant t-1
Le joueur 2 mise un euro a l`instant s quand le 0 s`affiche au lancer s-1. Il ne mise rien a l`instant s quand le 1 s`affiche a l`instant s-1
Des que le benefice cumule atteint 5 le joueur 1 ou 2 s`arrete de jouer et l`on note le nombre de lancers effectue. L`autre joueur 1 ou 2 continue de jouer jusqu`a atteindre le benefice de 5 ou plus. On note alors le nombre de lancers effectue pour le second joueur.
Le nombre de lancers est indefini dans cette seconde hypothese.
Tu verras un truc bizarre : le nombre de lancers requis pour avoir 2 benefs de 5 pour les 2 joueurs est tres peu variable.

tibo · 10-11-2014 16:20:50

Salut,

@yoshi : ou alors tu lui donne le script python et il se charge de le faire tourner?

@Bemo52 : Pour ton histoire de joueur qui attend le "bon" moment pour jouer, si les lancers sont indépendants, peu importe le résultat du lancer précédent, il aura toujours un chance sur deux de gagner.

Autre remarque, tu as parlé de roulette et de pair/impair. Attention, la proba de gagner n'est pas de 1/2, mais de 17/36. En effet, au jeu de la roulette, le zéro n'est ni pair, ni impair (ni rouge, ni noir).

Bemo52 · 10-11-2014 16:51:46

tibo a écrit :

Salut,
@yoshi : ou alors tu lui donne le script python et il se charge de le faire tourner?
@Bemo52 : Pour ton histoire de joueur qui attend le "bon" moment pour jouer, si les lancers sont indépendants, peu importe le résultat du lancer précédent, il aura toujours un chance sur deux de gagner.
Autre remarque, tu as parlé de roulette et de pair/impair. Attention, la proba de gagner n'est pas de 1/2, mais de 17/36. En effet, au jeu de la roulette, le zéro n'est ni pair, ni impair (ni rouge, ni noir).

Salut,

Je sais tout cela et tu ne m`apprend rien sauf que tu n`as toujours pas compris ce que je dis.
C`est un modele tres simplifie que je donne. Tu ne sais pas encore ou je vais.
La question n`est pas d`attendre le bon moment pour jouer. C`est une caricature de ce que j`ai propose. A aucun moment, je n`ai dit que c`est le bon moment pour jouer ou pas. J`ai decrit une methode de jeu tout simplement. Le resultat global des 2000 lancers donne un benefice global. Est-ce le fait du hasard ou est-ce le fait d`une structure cachee a decouvrir?
Je n`en sais rien mais j`ai mon idee.

Bref, merci pour tout.

Bemo52 · 10-11-2014 18:25:41

freddy a écrit :

Bemo52 a écrit :
Resalut,
Toujours pas de reponse?
La loi binomiale n`est pas la reponse a mon humble avis (houla, t'en es capable? )
Je me suis deja engueule avec un mec a ce sujet.
Le seul moyen de verifier cela est la simulation.
J`attends vos avis d`experts en la matiere.
Merci
Salut,
C'est bien cela le problème avec toi, aucun respect pour personne. Du coup, ici, t'es un peu tricard tant que tu ne changeras pas d'attitude envers les intervenants.
Pour la solution sans simulation, il suffit de développer la fonction génératrice de chaque essai et de répéter mille fois l'expérience.
Je pose [tex]p = \Pr (0)[/tex] dont je ne connais pas la valeur puisqu'on a aucune hypothèse sur l'équilibre de la pièce et on a :
[tex]G_X=\left(p+(1-p)\times \left(p+(1-p)\times X\right)\right)^{100}=\left(p(2-p)+(1-p)^2X\right)^{100}[/tex]
Et comme on vérifie que : [tex]p(2-p) + (1-p)^2 =1[/tex], à mon très humble avis, c'est bien une [tex]\mathcal{B}(p(2-p),\, 100)[/tex]

Maintenant que la simulation a ete faite merci Yoshi, j`attends toujours les chiffres donnes par la loi binomiale (3/4,100) p etant suppose egale a 1/2.
Merci

Bemo52 · 10-11-2014 19:06:31

Je veux bien que quelqu`un m`explique comment la loi binomiale s`applique au probleme que j`ai pose.
J`y tiens. J`ai ete banni d`un forum pour avoir ose dire non.
Que l`on me donne des chiffres et non des formules.
Je peux avoir les chiffres sur mon tableur ou ici :
http://jean-paul.davalan.pagesperso-ora … index.html

yoshi · 10-11-2014 19:40:04

Bonsoir,

Que tu tiennes à avoir une réponse, c'est normal ! Cette réponse serait instructive à beaucoup d'égards
Mais que tu dises :

J'ai ete banni d`un forum pour avoir ose dire non.

n'est pas exact, si tu parles de celui-ci...
Si tu parles de forum, donc, tu as eu droit à un "carton blanc", tu as été mis en "vacances" jusqu'au 1/11, mais pas parce que tu as "osé dire non"...
Non, absolument pas !
Je pensais qu'ayant profité de vacances ^_^, "du passé tu aurais fait table rase"...
Je souhaiterais donc que l'incident soit considéré comme clos et que ce ne soit plus évoqué surtout avec cette explication...

Est-ce que c'est assez clair ?

Merci d'avance...

Yoshi
- Modérateur -

Forum de mathématiques - Bibm@th.net

#1 07-11-2014 17:11:28

Probleme probas

#2 08-11-2014 16:23:10

Re : Probleme probas

#3 08-11-2014 19:27:57

Re : Probleme probas

#4 08-11-2014 21:49:56

Re : Probleme probas

#5 08-11-2014 21:55:55

Re : Probleme probas

#6 08-11-2014 21:57:22

Re : Probleme probas

#7 08-11-2014 22:00:19

Re : Probleme probas

#8 08-11-2014 22:01:21

Re : Probleme probas

#9 09-11-2014 00:33:28

Re : Probleme probas

#10 09-11-2014 01:01:21

Re : Probleme probas

#11 09-11-2014 13:19:25

Re : Probleme probas

#12 09-11-2014 18:50:32

Re : Probleme probas

#13 09-11-2014 21:14:02

Re : Probleme probas

#14 09-11-2014 21:28:30

Re : Probleme probas

#15 09-11-2014 21:55:45

Re : Probleme probas

#16 10-11-2014 10:23:17

Re : Probleme probas

#17 10-11-2014 13:35:56

Re : Probleme probas

#18 10-11-2014 14:25:46

Re : Probleme probas

#19 10-11-2014 15:55:53

Re : Probleme probas

#20 10-11-2014 16:19:23

Re : Probleme probas

#21 10-11-2014 16:20:50

Re : Probleme probas

#22 10-11-2014 16:51:46

Re : Probleme probas

#23 10-11-2014 18:25:41

Re : Probleme probas

#24 10-11-2014 19:06:31

Re : Probleme probas

#25 10-11-2014 19:40:04

Re : Probleme probas

Réponse rapide

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