G149 ‒ Gagner contre le hasard
Solution proposée par Thérèse Eveilleau
On trouvera à l'adresse http://therese.eveilleau.pagesperso-orange.fr/pages/truc_mat/textes/triplets.html une animation qui illustre les probabilités de gain de Zig selon les triplets d'entiers (x,y,2016 - x- - y) qu'il choisit.
CHANCES pour Zig de gagner CONTRE le hasard : modélisation Les points répondant au problème de coordonnées entières b1,b2,b3 avec (b1<= b2) ET
b3=2016-b1-b2 avec b3>=b2,
sont situés dans la lentille grise transparente en haut du triangle coloré des possibilités de jeux.
Les limites de la lentille, dont les chances de gagner sont de plus de 75% sont données par les couples à coordonnées entières, qui suivent :
[381,817] , [382,816] , [383,815] , [384,813] , [385,812] , [386,811] , [387,810] , [388,809] , [389,807] , [390,806] , [391, 805] , [392,804] , [393,803] , [394,802] , [395,801] , [396,800] , [397,799] , [398,798] , [399,797] , [400,796] , [401,795] , [402,794] , [403,794] , [404,793] , [405,792] , [406,791] , [407,790] , [408,789] , [409,789] , [410,788] , [411,787] , [412,786] , [413, 785] , [414,785] , [415,784] , [416,783] , [417,783] , [418,782] , [419,781] , [420,780] , [421,780] , [422,779] , [423,778] , [424,778] , [425,777] , [426,777] , [427,776] , [428,775] , [429,775] , [430,774] , [431,774] , [432,773] , [433,772] , [434,772] , [435, 771] , [436,771] , [437,770] , [438,770] , [439,769] , [440,769] , [441,768] , [442,768] , [443,767] , [444,766] , [445,766] , [446,765] , [447,765] , [448,765] , [449,764] , [450,764] , [451,763] , [452,763] , [453,762] , [454,762] , [455,761] , [456,761] , [457, 760] , [458,760] , [459,760] , [460,759] , [461,759] , [462,758] , [463,758] , [464,757] , [465,757] , [466,757] , [467,756] , [468,756] , [469,756] , [470,755] , [471,755] , [472,754] , [473,754] , [474,754] , [475,753] , [476,753] , [477,753] , [478,752] , [479, 752] , [480,751] , [481,751] , [482,751] , [483,750] , [484,750] , [485,750] , [486,749] , [487,749] , [488,749] , [489,748] , [490,748] , [491,748] , [492,748] , [493,747] , [494,747] , [495,747] , [496,746] , [497,746] , [498,746] , [499,745] , [500,745] , [501, 745] , [502,745] , [503,744] , [504,744] , [505,744] , [506,743] , [507,743] , [508,743] , [509,743] , [510,742] , [511,742] , [512,742] , [513,742] , [514,741] , [515,741] , [516,741] , [517,740] , [518,740] , [519,740] , [520,740] , [521,739] , [522,739] , [523, 739] , [524,739] , [525,739] , [526,738] , [527,738] , [528,738] , [529,738] , [530,737] , [531,737] , [532,737] , [533,737] , [534,736] , [535,736] , [536,736] , [537,736] , [538,736] , [539,735] , [540,735] , [541,735] , [542,735] , [543,734] , [544,734] , [545, 734] , [546,734] , [547,734] , [548,733] , [549,733] , [550,733]
Dans cette zone, on dénombre 2310 solutions donnant plus de 75% de chances de réussite.On peut choisir les 100 meilleures qui d'ailleurs excèdent toutes 76 %.
Les 100 meilleures solutions avec leur pourcentage sont les suivantes :
(466,775) --> 76.7629794973545 (464,776) --> 76.76209372637945 (468,774) --> 76.76179846938776 (462,777) --> 76.75943641345427 (470,773) --> 76.7588458994709 (460,778) --> 76.7547123015873 (472,772) --> 76.75382653061224 (458,779) --> 76.74821664777022 (474,771) --> 76.74703561980348 (456,780) --> 76.73965419501134 (476,770) --> 76.73817791005291 (454,781) --> 76.72932020030234 (478,769) --> 76.72754865835223 (452,782) --> 76.71691940665156 (465,775) --> 76.71691940665156 (467,774) --> 76.71632889266817 (463,776) --> 76.7157383786848 (480,768) --> 76.71485260770974 (469,773) --> 76.713671579743 (461,777) --> 76.71249055177627 (471,772) --> 76.70924272486772 (459,778) --> 76.70747118291762 (473,771) --> 76.70274707105064
(450,783) --> 76.70274707105064 (482,767) --> 76.70038501511716 (457,779) --> 76.70038501511716 (475,770) --> 76.69447987528345 (455,780) --> 76.69152730536659 (448,784) --> 76.68650793650794 (477,769) --> 76.68414588057445 (484,766) --> 76.68385062358277 (453,781) --> 76.68060279667422 (479,768) --> 76.67204034391534 (464,775) --> 76.6708593159486 (466,774) --> 76.67056405895691 (462,776) --> 76.66908777399848 (468,773) --> 76.66849726001512 (446,785) --> 76.66849726001512 (451,782) --> 76.66790674603175 (460,777) --> 76.66554469009826 (486,765) --> 76.66554469009826 (470,772) --> 76.66436366213152 (458,778) --> 76.65993480725623 (472,771) --> 76.6584585222978 (481,767) --> 76.65786800831444 (449,783) --> 76.65314389644747 (456,779) --> 76.65255338246409 (474,770) --> 76.6504865835223 (444,786) --> 76.6484197845805 (488,764) --> 76.64517195767196 (454,780) --> 76.64310515873017 (483,766) --> 76.64192413076341 (476,769) --> 76.64074310279668 (447,784) --> 76.63660950491308 (452,781) --> 76.6318853930461 (478,768) --> 76.62893282312925 (442,787) --> 76.62657076719577 (465,774) --> 76.62509448223734 (463,775) --> 76.62479922524565 (485,765) --> 76.62391345427059 (467,773) --> 76.62332294028722 (490,763) --> 76.62302768329555 (461,776) --> 76.62273242630386 (469,772) --> 76.619779856387 (459,777) --> 76.61859882842026 450,782) --> 76.61859882842026 (445,785) --> 76.61800831443689 (480,767) --> 76.61535100151171 (471,771) --> 76.61416997354497 (457,778) --> 76.61269368858655 (473,770) --> 76.60678854875283 (455,779) --> 76.60472174981103 (487,764) --> 76.60413123582767 (448,783) --> 76.6035407218443 (440,788) --> 76.60265495086924 (482,766) --> 76.59970238095238 (492,762) --> 76.59881660997732 (443,786) --> 76.59763558201058 (475,769) --> 76.59734032501889 (453,780) --> 76.59497826908542 (446,784) --> 76.58641581632654 (477,768) --> 76.58612055933484 (451,781) --> 76.58316798941799 (489,763) --> 76.58228221844293 (484,765) --> 76.58228221844293 (464,774) --> 76.57932964852608 (462,775) --> 76.5787391345427 (466,773) --> 76.57814862055933 (438,789) --> 76.5769675925926
(460,776) --> 76.57608182161754 (441,787) --> 76.57519605064248 (468,772) --> 76.5749007936508 (494,761) --> 76.572833994709 (479,767) --> 76.572833994709 (458,777) --> 76.57165296674225 (470,771) --> 76.56988142479214 (449,782) --> 76.56958616780045 (444,785) --> 76.56751936885865 (456,778) --> 76.56515731292517 (472,770) --> 76.56279525699169
Voici la liste des 2310 solutions :
[381,817] , [382,817] , [382,816] , [383,816] , [383,815] , [384,816] , [384,815] , [384,814] , [38 4,813] , [385,815] , [385,814] , [385,813] , [385,812] , [386,815] , [386,814] , [386,813] , [386,812] , [386,811] , [387,814] , [387,813] , [387,812] , [387, 811] , [387,810] , [388,814] , [388,813] , [388,812] , [388,811] , [388,810] , [388,809] , [389,813] , [389,812] , [389,811] , [389,810] , [389,809] , [389,808] , [389,807] , [390,813] , [390,812] , [390,811] , [390,810] , [390,809] , [390,808] , [390,807] , [390, 806] , [391,812] , [391,811] , [391,810] , [391,809] , [391,808] , [391,807] , [391,806] , [391,805] , [392,812] , [392,811] , [392,810] , [392,809] , [392,808] , [392,807] , [392,806] , [392,805] , [392,804] , [393,811] , [393,810] , [393,809] , [393,808] , [393, 807] , [393,806] , [393,805] , [393,804] , [393,803] , [394,811] , [394,810] , [394,809] , [394,808] , [394,807] , [394,806] , [394,805] , [394,804] , [394,803] , [394,802] , [395,810] , [395,809] , [395,808] , [395,807] , [395,806] , [395,805] , [395,804] , [395, 803] , [395,802] , [395,801] , [396,810] , [396,809] , [396,808] , [396,807] , [396,806] , [396,805] , [396,804] , [396,803] , [396,802] , [396,801] , [396,800] , [397,809] , [397,808] , [397,807] , [397,806] , [397,805] , [397,804] , [397,803] , [397,802] , [397, 801] , [397,800] , [397,799] , [398,809] , [398,808] , [398,807] , [398,806] , [398,805] , [398,804] , [398,803] , [398,802] , [398,801] , [398,800] , [398,799] , [398,798] , [399,808] , [399,807] , [399,806] , [399,805] , [399,804] , [399,803] , [399,802] , [399, 801] , [399,800] , [399,799] , [399,798] , [399,797] , [400,808] , [400,807] , [400,806] , [400,805] , [400,804] , [400,803] , [400,802] , [400,801] , [400,800] , [400,799] , [400,798] , [400,797] , [400,796] , [401,807] , [401,806] , [401,805] , [401,804] , [401, 803] , [401,802] , [401,801] , [401,800] , [401,799] , [401,798] , [401,797] , [401,796] , [401,795] , [402,807] , [402,806] , [402,805] , [402,804] , [402,803] , [402,802] , [402,801] , [402,800] , [402,799] , [402,798] , [402,797] , [402,796] , [402,795] , [402, 794] , [403,806] , [403,805] , [403,804] , [403,803] , [403,802] , [403,801] , [403,800] , [403,799] , [403,798] , [403,797] , [403,796] , [403,795] , [403,794] , [404,806] , [404,805] , [404,804] , [404,803] , [404,802] , [404,801] , [404,800] , [404,799] , [404, 798] , [404,797] , [404,796] , [404,795] , [404,794] , [404,793] , [405,805] , [405,804] , [405,803] , [405,802] , [405,801] , [405,800] , [405,799] , [405,798] , [405,797] , [405,796] , [405,795] , [405,794] , [405,793] , [405,792] , [406,805] , [406,804] , [406, 803] , [406,802] , [406,801] , [406,800] , [406,799] , [406,798] , [406,797] , [406,796] , [406,795] , [406,794] , [406,793] , [406,792] , [406,791] , [407,804] , [407,803] , [407,802] , [407,801] , [407,800] , [407,799] , [407,798] , [407,797] , [407,796] , [407, 795] , [407,794] , [407,793] , [407,792] , [407,791] , [407,790] , [408,804] , [408,803] , [408,802] , [408,801] , [408,800] , [408,799] , [408,798] , [408,797] , [408,796] , [408,795] , [408,794] , [408,793] , [408,792] , [408,791] , [408,790] , [408,789] , [409, 803] , [409,802] , [409,801] , [409,800] , [409,799] , [409,798] , [409,797] , [409,796] , [409,795] , [409,794] , [409,793] , [409,792 ] , [409,791] , [409,790] , [409,789] , [410,803] , [410,802] , [410,801] , [410,800] , [410,799] , [410,798] , [410,797] , [410, 796] , [410,795] , [410,794] , [410,793] , [410,792] , [410,791] , [410,790] , [410,789] , [410,788] , [411,802] , [411,801] , [411, 800] , [411,799] , [411,798] , [411,797] , [411,796] , [411,795] , [411,794] , [411,793] , [411,792] , [411,791] , [411,790] , [411,789] , [411,788] , [411,787] , [412,802] , [412,801] , [412,800] , [412,799] , [412,798] , [412,797] , [412,796] , [412,795] , [412, 794] , [412,793] , [412,792] , [412,791] , [412,790] , [412,789] , [412,788] , [412,787] , [412,786] , [413,801] , [41 3,800] , [413,799] , [413,798] , [413,797] , [413,796] , [413,795] , [413,794] , [413,793] , [413,792] , [413,791] , [413,790] , [413,789] , [413, 788] , [413,787] , [413,786] , [413,785] , [414,801] , [414,800] , [414,799] , [414,798] , [414,797] , [414,79 6] , [414,795] , [414,794] , [414,793] , [414,792] , [414,791] , [414,790] , [414,789] , [414,788] , [414,787] , [414,786] , [414,785] , [415,800] , [415, 799] , [415,798] , [415,797] , [415,796] , [415,795] , [415,794] , [415,793] , [415,792] , [415,791] , [415,790] , [415,789] , [415,788] , [415,787] , [415,786] , [415,785] , [415,784] , [416,800] , [416,799] , [416,798] , [416,797] , [416,796] , [416,795] , [416, 794] , [416,793] , [416,792] , [416,791] , [416,790] , [416,789] , [416,788] , [416,787] , [416,786] , [416,785] , [416,784] , [416,783] , [417,799] , [417,798] , [417,797] , [417,796] , [417,795] , [417,794] , [417,793] , [417,792] , [417,791] , [417,790] , [417, 789] , [417,788] , [417,787] , [417,786] , [417,785] , [417,784] , [417,783] , [418,799] , [418,798] , [418,797] , [418,796] , [418,795] , [418,794] , [418,793] , [418,792] , [418,791] , [418,790] , [418,789] , [418,788] , [418,787] , [418,786] , [418,785] , [418, 784] , [418,783] , [418,782] , [419,798] , [419,797] , [419,796] , [419,795] , [419,794] , [419,793] , [419,792] , [419,791] , [419,790] , [419,789] , [419,788] , [419,787] , [419,786] , [419,785] , [419,784] , [419,783] , [419,782] , [419,781] , [420,798] , [420, 797] , [420,796] , [420,795] , [420,794] , [420,793] , [420,792] , [420,791] , [420,790] , [420,789] , [420,788] , [420,787] , [420,786] , [420,785] , [420,784] , [420,783] , [420,782] , [420,781] , [420,780] , [421,797] , [421,796] , [421,795] , [421,794] , [421, 793] , [421,792] , [421,791] , [421,790] , [421,789] , [421,788] , [421,787] , [421,786] , [421,785] , [421,784] , [421,783] , [421,782] , [421,781] , [421,780] , [422,797] , [422,796] , [422,795] , [422,794] , [422,793] , [422,792] , [422,791] , [422,790] , [422, 789] , [422,788] , [422,787] , [422,786] , [422,785] , [422,784] , [422,783] , [422,782] , [422,781] , [422,780] , [422,779] , [423,796] , [423,795] , [423,794] , [423,793] , [423,792] , [423,791] , [423,790] , [423,789] , [423,788] , [423,787] , [423,786] , [423, 785] , [423,784] , [423,783] , [423,782] , [423,781] , [423,780] , [423,779] , [423,778] , [424,796] , [424,795] , [424,794] , [424,793] , [424,792] , [424,791] , [424,790] , [424,789] , [424,788] , [424,787] , [424,786] , [424,785] , [424,784] , [424,783] , [424, 782] , [424,781] , [424,780] , [424,779] , [424,778] , [425,795] , [425,794] , [425,793] , [425,792] , [425,791] , [425,790] , [425,789] , [425,788] , [425,787] , [425,786] , [425,785] , [425,784] , [425,783] , [425,782] , [425,781] , [425,780] , [425,779] , [425, 778] , [425,777] , [426,795] , [426,794] , [426,793] , [426,792] , [426,791] , [426,790] , [426,789] , [426,788] , [426,787] , [426,786] ,
[426,785] , [426,784] , [426,783] , [426,782] , [426,781] , [426,780] , [426,779] , [426,778] , [426,777] , [427,794] , [427, 793] , [427,792] , [427,791] , [427,790] , [427,789] , [427,788] , [427,787] , [427,786] , [427,785] , [427,784] , [427,783] , [427,782] , [427,781] , [427,780] , [427,779] , [427,778] , [427,777] , [427,776] , [428,794] , [428,793] , [428,792] , [428,791] , [428, 790] , [428,789] , [428,788] , [428,787] , [428,786] , [428,785] , [428,784] , [428,783] , [428,782] , [428,781] , [428,780] , [428,779] , [428,778] , [428,777] , [428,776] , [428,775] , [429,793] , [429,792] , [429,791] , [429,790] , [429,789] , [429,788] , [429, 787] , [429,786] , [429,785] , [429,784] , [429,783] , [429,782] , [429,781] , [429,780] , [429,779] , [429,778] , [429,777] , [429, 776] , [429,775] , [430,793] , [430,792] , [430,791] , [430,790] , [430,789] , [430,788] , [430,787] , [430,786] , [430,785] , [43 0,784] , [430,783] , [430,782] , [430,781] , [430,780] , [430,779] , [430,778] , [430,777] , [430,776] , [430,775] , [430,774] , [431, 792] , [431,791] , [431,790] , [431,789] , [431,788] , [431,787] , [431,786] , [431,785] , [431,784] , [431,783] , [431,78 2] , [431,781] , [431,780] , [431,779] , [431,778] , [431,777] , [431,776] , [431,775] , [431,774] , [432,792] , [432,791] , [432,790] , [432, 789] , [432,788] , [432,787] , [432,786] , [432,785] , [432,784] , [432,783] , [432,782] , [432,781] , [432,780] , [432,779] , [432,778] , [432,777] , [432,776] , [432,775] , [432,774] , [432,773] , [433,791] , [433,790] , [433,789] , [433,788] , [433,787] , [433, 786] , [433,785] , [433,784] , [433,783] , [433,782] , [433,781] , [433,780] , [433,779] , [433,778] , [43 3,777] , [433,776] , [433,775] , [433,774] , [433,773] , [433,772] , [434,791] , [434,790] , [434,789] , [434,788] , [434,787] , [434,786] , [434,785] , [434, 784] , [434,783] , [434,782] , [434,781] , [434,780] , [434,779] , [434,778] , [434,777] , [434,776] , [434,775] , [434,774] , [434,773] , [434,772] , [435,790] , [435,789] , [435,788] , [435,787] , [435,786] , [435,785] , [435,784] , [435,783] , [435,782] , [435, 781] , [435,780] , [435,779] , [435,778] , [435,777] , [435,776] , [435,775] , [435,774] , [435,773] , [435,772] , [435,771] , [436,790] , [436,789] , [436,788] , [436,787] , [436,786] , [436,785] , [436,784] , [436,783] , [436,782] , [436,781] , [436,780] , [436, 779] , [436,778] , [436,777] , [436,776] , [436,775] , [436,774] , [436,773] , [436,772] , [436,771] , [437,789] , [437,788] , [437,787] , [437,786] , [437,785] , [437,784] , [437,783] , [437,782] , [437,781] , [437,780] , [437,779] , [437,778] , [437,777] , [437, 776] , [437,775] , [437,774] , [437,773] , [437,772] , [437,771] , [437,770] , [438,789] , [438,788] , [438,787] , [438,786] , [438,785] , [438,784] , [438,783] , [438,782] , [438,781] , [438,780] , [438,779] , [438,778] , [438,777] , [438,776] , [438,775] , [438, 774] , [438,773] , [438,772] , [438,771] , [438,770] , [439,788] , [439,787] , [439,786] , [439,785] , [439,784] , [439,783] , [439,782] , [439,781] , [439,780] , [439,779] , [439,778] , [439,777] , [439,776] , [439,775] , [439,774] , [439,773] , [439,772] , [439, 771] , [439,770] , [439,769] , [440,788] , [440,787] , [440,786] , [440,785] , [440,784] , [440,783] , [440,782] , [440,781] , [440,780] , [440,779] , [440,778] , [440,777] , [440,776] , [440,775] , [440,774] , [440,773] , [440,772] , [440,771] , [440,770] , [440, 769] , [441,787] , [441,786] , [441,785] , [441,784] , [441,783] , [441,782] , [441,781] , [441,780] , [441,779] , [441,778] , [441,777] , [441,776] , [441,775] , [441,774] , [441,773] , [441,772] , [441,771] , [441,770] , [441,769] , [441,768] , [442,787] , [442, 786] , [442,785] , [442,784] , [442,783] , [442,782] , [442,781] , [442,780] , [442,779] , [442,778] , [442,777] , [442,776] , [442,775] , [442,774] , [442,773] , [442,772] , [442,771] , [442,770] , [442,769] , [442,768] , [443,786] , [443,785] , [443,784] , [443, 783] , [443,782] , [443,781] , [443,780] , [443,779] , [443,778] , [443,777] , [443,776] , [443,775] , [443,774] , [443,773] , [443,772] , [443,771] , [443,770] , [443,769] , [443,768] , [443,767] , [444,786] , [444,785] , [444,784] , [444,783] , [444,782] , [444, 781] , [444,780] , [444,779] , [444,778] , [444,777] , [444,776] , [444,775] , [444,774] , [444,773] , [444,772] , [444,771] , [444,770] , [444,769] , [444,768] , [444,767] , [444,766] , [445,785] , [445,784] , [445,783] , [445,782] , [445,781] , [445,780] , [445, 779] , [445,778] , [445,777] , [445,776] , [445,775] , [445,774] , [445,773] , [445,772] , [445,771] , [445,770] , [445,769] , [445,768] , [445,767] , [445,766] , [446,785] , [446,784] , [446,783] , [446,782] , [446,781] , [446,780] , [446,779] , [446,778] , [446, 777] , [446,776] , [446,775] , [446,774] , [446,773] , [446,772] , [446,771] , [446,770] , [446,769] , [446,768] , [446,767] , [446,766 ] , [446,765] , [447,784] , [447,783] , [447,782] , [447,781] , [447,780] , [447,779] , [447,778] , [447,777] , [447,776] , [447, 775] , [447,774] , [447,773] , [447,772] , [447,771] , [447,770] , [447,769] , [447,768] , [447,767] , [447,766] , [447,765] , [448, 784]
,[448,783] , [448,782] , [448,781] , [448,780] , [448,779] , [448,778] , [448,777] , [448,776] , [448,775] , [448,774] , [448,773] , [448,772] , [448,771] , [448,770] , [448,769] , [448,768] , [448,767] , [448,766] , [448,765] , [449,783] , [449,782] , [449, 781] , [449,780] , [449,779] , [449,778] , [449,777] , [449,776] , [449,775] , [449,774] , [449,773] , [449,772] , [449 ,771] , [449,770] , [449,769] , [449,768] , [449,767] , [449,766] , [449,765] , [449,764] , [450,783] , [450,782] , [450,781] , [450,780] , [450, 779] , [450,778] , [450,777] , [450,776] , [450,775] , [450,774] , [450,773] , [450,772] , [450,771] , [450,770 ] , [450,769] , [450,768] , [450,767] , [450,766] , [450,765] , [450,764] , [451,782] , [451,781] , [451,780] , [451,779] , [451,778] , [451,777] , [451, 776] , [451,775] , [451,774] , [451,773] , [451,772] , [451,771] , [451,770] , [451,769] , [451,768] , [451,767] , [451,766] , [451,765] , [451,764] , [451,763] , [452,782] , [452,781] , [452,780] , [452,779] , [452,778] , [452,777] , [452,776] , [452,775] , [452, 774] , [452,773] , [452,772] , [452,771] , [452,770] , [452,769] , [452,768] , [452,767] , [452,766] , [452,765] , [452,764] , [452,763] , [453,781] , [453,780] , [453,779] , [453,778] , [453,777] , [453,776] , [453,775] , [453,774] , [453,773] , [453,772] , [453, 771] , [453,770] , [453,769] , [453,768] , [453,767] , [453,766] , [453,765] , [453,764] , [453,763] , [453,762] , [454,781] , [454,780] , [454,779] , [454,778] , [454,777] , [454,776] , [454,775] , [454,774] , [454,773] , [454,772] , [454,771] , [454,770] , [454, 769] , [454,768] , [454,767] , [454,766] , [454,765] , [454,764] , [454,763] , [454,762] , [455,780] , [455,779] , [455,778] , [455,777] , [455,776] , [455,775] , [455,774] , [455,773] , [455,772] , [455,771] , [455,770] , [455,769] , [455,768] , [455,767] , [455, 766] , [455,765] , [455,764] , [455,763] , [455,762] , [455,761] , [456,780] , [456,779] , [456,778] , [456,777] , [456,776] , [456,775] , [456,774] , [456,773] , [456,772] , [456,771] , [456,770] , [456,769] , [456,768] , [456,767] , [456,766] , [456,765] , [456, 764] , [456,763] , [456,762] , [456,761] , [457,779] , [457,778] , [457,777] , [457,776] , [457,775] , [457,774] , [457,773] , [457,772] , [457,771] , [457,770] , [457,769] , [457,768] , [457,767] , [457,766] , [457,765] , [457,764] , [457,763] , [457,762] , [457, 761] , [457,760] , [458,779] , [458,778] , [458,777] , [458,776] , [458,775] , [458,774] , [458,773] , [458,772] , [458,771] , [458,770] , [458,769] , [458,768] , [458,767] , [458,766] , [458,765] , [458,764] , [458,763] , [458,762] , [458,761] , [458,760] , [459, 778] , [459,777] , [459,776] , [459,775] , [459,774] , [459,773] , [459,772] , [459,771] , [459,770] , [459,769] , [459,768] , [459,767] , [459,766] , [459,765] , [459,764] , [459,763] , [459,762] , [459,761] , [459,760] , [460,778] , [460,777] , [460,776] , [460, 775] , [460,774] , [460,773] , [460,772] , [460,771] , [460,770] , [460,769] , [460,768] , [460,767] , [460,766] , [460,765] , [460,764] , [460,763] , [460,762] , [460,761] , [460,760] , [460,759] , [461,777] , [461,776] , [461,775] , [461,774] , [461,773] , [461, 772] , [461,771] , [461,770] , [461,769] , [461,768] , [461,767] , [461,766] , [461,765] , [461,764] , [461,763] , [461,762] , [461,761] , [461,760] , [461,759] , [462,777] , [462,776] , [462,775] , [462,774] , [462,773] , [462,772] , [462,771] , [462,770] , [462, 769] , [462,768] , [462,767] , [462,766] , [462,765] , [462,764] , [462,763] , [462,762] , [462,761] , [462,760] , [462,759] , [462,758] ,
[463,776] , [463,775] , [463,774] , [463,773] , [463,772] , [463,771] , [463,770] , [463,769] , [463,768] , [463,767] , [463, 766] , [463,765] , [463,764] , [463,763] , [463,762] , [463,761] , [463,760] , [463,759] , [463,758] , [464,776] , [464,775] , [464,774] , [464,773] , [464,772] , [464,771] , [464,770] , [464,769] , [464,768] , [464,767] , [464,766] , [464,765] , [464,764] , [464, 763] , [464,762] , [464,761] , [464,760] , [464,759] , [464,758] , [464,757] , [465,775] , [465,774] , [465,773] , [465,772] , [465, 771] , [465,770] , [465,769] , [465,768] , [465,767] , [465,766] , [465,765] , [465,764] , [465,763] , [465,762] , [465,761] , [465 ,760] , [465,759] , [465,758] , [465,757] , [466,775] , [466,774] , [466,773] , [466,772] , [466,771] , [466,770] , [466,769] , [466, 768] , [466,767] , [466,766] , [466,765] , [466,764] , [466,763] , [466,762] , [466,761] , [466,760] , [466,759] , [466,758 ] , [466,757] , [467,774] , [467,773] , [467,772] , [467,771] , [467,770] , [467,769] , [467,768] , [467,767] , [467,766] , [467,765] , [467, 764] , [467,763] , [467,762] , [467,761] , [467,760] , [467,759] , [467,758] , [467,757] , [467,756] , [468,774] , [468,773] , [468,772] , [468,771] , [468,770] , [468,769] , [468,768] , [468,767] , [468,766] , [468,765] , [468,764] , [468,763] , [468,762] , [468, 761] , [468,760] , [468,759] , [468,758] , [468,757] , [468,756] , [469,773] , [469,772] , [469,771] , [469 ,770] , [469,769] , [469,768] , [469,767] , [469,766] , [469,765] , [469,764] , [469,763] , [469,762] , [469,761] , [469,760] , [469,759] , [469,758] , [469, 757] , [469,756] , [470,773] , [470,772] , [470,771] , [470,770] , [470,769] , [470,768] , [470,767] , [470,766] , [470,765] , [470,764] , [470,763] , [470,762] , [470,761] , [470,760] , [470,759] , [470,758] , [470,757] , [470,756] , [470,755] , [471,772] , [471, 771] , [471,770] , [471,769] , [471,768] , [471,767] , [471,766] , [471,765] , [471,764] , [471,763] , [471,762] , [471,761] , [471,760] , [471,759] , [471,758] , [471,757] , [471,756] , [471,755] , [472,772] , [472,771] , [472,770] , [472,769] , [472,768] , [472, 767] , [472,766] , [472,765] , [472,764] , [472,763] , [472,762] , [472,761] , [472,760] , [472,759] , [472,758] , [472,757] , [472,756] , [472,755] , [472,754] , [473,771] , [473,770] , [473,769] , [473,768] , [473,767] , [473,766] , [473,765] , [473,764] , [473, 763] , [473,762] , [473,761] , [473,760] , [473,759] , [473,758] , [473,757] , [473,756] , [473,755] , [473,754] , [474,771] , [474,770] , [474,769] , [474,768] , [474,767] , [474,766] , [474,765] , [474,764] , [474,763] , [474,762] , [474,761] , [474,760] , [474, 759] , [474,758] , [474,757] , [474,756] , [474,755] , [474,754] , [475,770] , [475,769] , [475,768] , [475,767] , [475,766] , [475,765] , [475,764] , [475,763] , [475,762] , [475,761] , [475,760] , [475,759] , [475,758] , [475,757] , [475,756] , [475,755] , [475, 754] , [475,753] , [476,770] , [476,769] , [476,768] , [476,767] , [476,766] , [476,765] , [476,764] , [476,763] , [476,762] , [476,761] , [476,760] , [476,759] , [476,758] , [476,757] , [476,756] , [476,755] , [476,754] , [476,753] , [477,769] , [477,768] , [477, 767] , [477,766] , [477,765] , [477,764] , [477,763] , [477,762] , [477,761] , [477,760] , [477,759] , [477,758] , [477,757] , [477,756] , [477,755] , [477,754] , [477,753] , [478,769] , [478,768] , [478,767] , [478,766] , [478,765] , [478,764] , [478,763] , [478, 762] , [478,761] , [478,760] , [478,759] , [478,758] , [478,757] , [478,756] , [478,755] , [478,754] , [478,753] , [478,752] , [479,768] , [479,767] , [479,766] , [479,765] , [479,764] , [479,763] , [479,762] , [479,761] , [479,760] , [479,759] , [479,758] , [479, 757] , [479,756] , [479,755] , [479,754] , [479,753] , [479,752] , [480,768] , [480,767] , [480,766] , [480,765] , [480,764] , [480,763] , [480,762] , [480,761] , [480,760] , [480,759] , [480,758] , [480,757] , [480,756] , [480,755] , [480,754] , [480,753] , [480, 752] , [480,751] , [481,767] , [481,766] , [481,765] , [481,764] , [481,763] , [481,762] , [481,761] , [481,760] , [481,759] , [481,758] , [481,757] , [481,756] , [481,755] , [481,754] , [481,753] , [481,752] , [481,751] , [482,767] , [482,766] , [482,765] , [482, 764] , [482,763] , [482,762] , [482,761] , [482,760] , [482,759] , [482,758] , [482,757] , [482,756] , [482,755] , [482,754] , [482,753] , [482,752] , [482,751] , [483,766] , [483,765] , [483,764] , [483,763] , [483,762] , [483,761] , [483,760] , [483,759] , [483, 758] , [483,757] , [483,756] , [483,755] , [483,754] , [483,753] , [483,752] , [483,751] , [483,750] , [484,766] , [484,765] , [484,764] , [484,763] , [484,762] , [484,761] , [484,760] , [484,759] , [484,758] , [484,757] , [484,756] , [484,755] , [484,754] , [484, 753] , [484,752] , [484,751] , [484,750] , [485,765] , [485,764] , [485,763] , [485,762] , [485,761] , [485,760] , [485,759] , [485, 758] , [485,757] , [485,756] , [485,755] , [485,754] , [485,753] , [485,752] , [485,751] , [485,750] , [486,765] , [486,764] , [486,763] , [486,762] , [486,761] , [486,760] , [486,759] , [486,758] , [486,757] , [486,756] , [486,755] , [486,754] , [486,753] , [486, 752] , [486,751] , [486,750] , [486,749] , [487,764] , [487,763] , [487,762] , [487,761] , [487,760] , [487,759] , [487 ,758] , [487,757] , [487,756] , [487,755] , [487,754] , [487,753] , [487,752] , [487,751] , [487,750] , [487,749] , [488,764] , [488,763] , [488, 762] , [488,761] , [488,760] , [488,759] , [488,758] , [488,757] , [488,756] , [488,755] , [488,754] , [488,753 ] , [488,752] , [488,751] , [488,750] , [488,749] , [489,763] , [489,762] , [489,761] , [489,760] , [489,759] , [489,758] , [489,757] , [489,756] , [489, 755] , [489,754] , [489,753] , [489,752] , [489,751] , [489,750] , [489,749] , [489,748] , [490,763] , [490,762] , [490,761] , [490,760] , [490,759] , [490,758] , [490,757] , [490,756] , [490,755] , [490,754] , [490,753] , [490,752] , [490,751] , [490,750] , [490, 749] , [490,748] , [491,762] , [491,761] , [491,760] , [491,759] , [491,758] , [491,757] , [491,756] , [491,755] , [491,754] , [491,753] , [491,752] , [491,751] , [491,750] , [491,749] , [491,748] , [492,762] , [492,761] , [492,760] , [492,759] , [492,758] , [492, 757] , [492,756] , [492,755] , [492,754] , [492,753] , [492,752] , [492,751] , [492,750] , [492,749] , [492,748] , [493,761] , [493,760] , [493,759] , [493,758] , [493,757] , [493,756] , [493,755] , [493,754] , [493,753] , [493,752] , [493,751] , [493,750] , [493, 749] , [493,748] , [493,747] , [494,761] , [494,760] , [494,759] , [494,758] , [494,757] , [494,756] , [494,755] , [494,754] , [494,753] , [494,752] , [494,751] , [494,750] , [494,749] , [494,748] , [494,747] , [495,760] , [495,759] , [495,758] , [495,757] , [495, 756] , [495,755] , [495,754] , [495,753] , [495,752] , [495,751] , [495,750] , [495,749] , [495,748] , [495,747] , [496,760] , [496,759] , [496,758] , [496,757] , [496,756] , [496,755] , [496,754] , [496,753] , [496,752] , [496,751] , [496,750] , [496,749] , [496, 748] , [496,747] , [496,746] , [497,759] , [497,758] , [497,757] , [497,756] , [497,755] , [497,754] , [497,753] , [497,752] , [497,751] , [497,750] , [497,749] , [497,748] , [497,747] , [497,746] , [498,759] , [498,758] , [498,757] , [498,756] , [498,755] , [498, 754] , [498,753] , [498,752] , [498,751] , [498,750] , [498,749] , [498,748] , [498,747] , [498,746] , [499,758] , [499,757] , [499,756] , [499,755] , [499,754] , [499,753] , [499,752] , [499,751] , [499,750] , [499,749] , [499,748] , [499,747] , [499,746] , [499, 745] , [500,758] , [500,757] , [500,756] , [500,755] , [500,754] , [500,753] , [500,752] , [500,751] , [500,750] , [500,749] , [500,748] , [500,747] , [500,746] , [500,745] , [501,757] , [501,756] , [501,755] , [501,754] , [501,753] , [501,752] , [501,751] , [501, 750] , [501,749] , [501,748] , [501,747] , [501,746] , [501,745] , [502,757] , [502,756] , [502,755] , [502,754] , [502,753] , [502,752] , [502,751] , [502,750] , [502,749] , [502,748] , [502,747] , [502,746] , [502,745] , [503,756] , [503,755] , [503,754] , [503, 753] , [503,752] , [503,751] , [503,750] , [503,749] , [503,748] , [503,747] , [503,746] , [503,745] , [503,744] , [504,756] , [504,755] , [504,754] , [504,753] , [504,752] , [504,751] , [504,750] , [504,749] , [504,748] , [504,747] , [504,746] , [504,745] , [504, 744] , [505,755] , [505,754] , [505,753] , [505,752] , [505,751] , [505,750] , [505,749] , [505,748] , [505,747] , [505,746] , [505,745] , [505,744] , [506,755] , [506,754] , [506,753] , [506,752] , [506,751] , [506,750] , [506,749] , [506,748] , [506,747] , [506, 746] , [506,745] , [506,744] , [506,743] , [507,754] , [507,753] , [507,752] , [507,751] , [507,750] , [507,749] , [507,748] , [507,747] ,
[507,746] , [507,745] , [507,744] , [507,743] , [508,754] , [508,753] , [508,752] , [508,751] , [508,750] , [508,749] , [508, 748] , [508,747] , [508,746] , [508,745] , [508,744] , [508,743] , [509,753] , [509,752] , [509,751] , [509,750] , [509,749] , [509, 748] , [509,747] , [509,746] , [509,745] , [509,744] , [509,743] , [510,753] , [510,752] , [510,751] , [510,750] , [510,749] , [510 ,748] , [510,747] , [510,746] , [510,745] , [510,744] , [510,743] , [510,742] , [511,752] , [511,751] , [511,750] , [511,749] , [511, 748] , [511,747] , [511,746] , [511,745] , [511,744] , [511,743] , [511,742] , [512,752] , [512,751] , [512,750] , [512,749 ] , [512,748] , [512,747] , [512,746] , [512,745] , [512,744] , [512,743] , [512,742] , [513,751] , [513,750] , [513,749] , [513,748] , [513, 747] , [513,746] , [513,745] , [513,744] , [513,743] , [513,742] , [514,751] , [514,750] , [514,749] , [514,748] , [514,747] , [514,746] , [514,745] , [514,744] , [514,743] , [514,742] , [514,741] , [515,750] , [515,749] , [515,748] , [515,747] , [515,746] , [515, 745] , [515,744] , [515,743] , [515,742] , [515,741] , [516,750] , [516,749] , [516,748] , [516,747] , [516 ,746] , [516,745] , [516,744] , [516,743] , [516,742] , [516,741] , [517,749] , [517,748] , [517,747] , [517,746] , [517,745] , [517,744] , [517,743] , [517, 742] , [517,741] , [517,740] , [518,749] , [518,748] , [518,747] , [518,746] , [518,745] , [518,744] , [518,743] , [518,742] , [518,741] , [518,740] , [519,748] , [519,747] , [519,746] , [519,745] , [519,744] , [519,743] , [519,742] , [519,741] , [519,740] , [520, 748] , [520,747] , [520,746] , [520,745] , [520,744] , [520,743] , [520,742] , [520,741] , [520,740] , [521,747] , [521,746] , [521,745] , [521,744] , [521,743] , [521,742] , [521,741] , [521,740] , [521,739] , [522,747] , [522,746] , [522,745] , [522,744] , [522, 743] , [522,742] , [522,741] , [522,740] , [522,739] , [523,746] , [523,745] , [523,744] , [523,743] , [523,742] , [523,741] , [523,740] , [523,739] , [524,746] , [524,745] , [524,744] , [524,743] , [524,742] , [524,741] , [524,740] , [524,739] , [525,745] , [525, 744] , [525,743] , [525,742] , [525,741] , [525,740] , [525,739] , [526,745] , [526,744] , [526,743] , [526,742] , [526,741] , [526,740] , [526,739] , [526,738] , [527,744] , [527,743] , [527,742] , [527,741] , [527,740] , [527,739] , [527,738] , [528,744] , [528, 743] , [528,742] , [528,741] , [528,740] , [528,739] , [528,738] , [529,743] , [529,742] , [529,741] , [529,740] , [529,739] , [529,738] , [530,743] , [530,742] , [530,741] , [530,740] , [530,739] , [530,738] , [530,737] , [531,742] , [531,741] , [531,740] , [531, 739] , [531,738] , [531,737] , [532,742] , [532,741] , [532,740] , [532,739] , [532,738] , [532,737] , [533,741] , [533,740] , [533,739] , [533,738] , [533,737] , [534,741] , [534,740] , [534,739] , [534,738] , [534,737] , [534,736] , [535,740] , [535,739] , [535, 738] , [535,737] , [535,736] , [536,740] , [536,739] , [536,738] , [536,737] , [536,736] , [537,739] , [537,738] , [537,737] , [537,736] , [538,739] , [538,738] , [538,737] , [538,736] , [539,738] , [539,737] , [539,736] , [539,735] , [540,738] , [540,737] , [540, 736] , [540,735] , [541,737] , [541,736] , [541,735] , [542,737] , [542,736] , [542,735] , [543,736] , [543,735] , [543,734] , [544,736] , [544,735] , [544,734] , [545,735] , [545,734] , [546,735] , [546,734] , [547,734] , [548,734] , [548,733] , [549,733] , [550, 733]
