Created
January 14, 2009 16:04
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A Python solution to Project Euler Problem 99
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""" Project Euler Problem 99 http://projecteuler.net/index.php?section=problems&id=99 """ | |
def max_base_exp(base_exps): | |
from math import log | |
return reduce(lambda a, b: a if a[2] * log(a[1]) > b[2] * log(b[1]) else b, base_exps) | |
print max_base_exp([ | |
(1, 519432, 525806), | |
(2, 632382, 518061), | |
(3, 78864, 613712), | |
(4, 466580, 530130), | |
(5, 780495, 510032), | |
(6, 525895, 525320), | |
(7, 15991, 714883), | |
(8, 960290, 502358), | |
(9, 760018, 511029), | |
(10, 166800, 575487), | |
(11, 210884, 564478), | |
(12, 555151, 523163), | |
(13, 681146, 515199), | |
(14, 563395, 522587), | |
(15, 738250, 512126), | |
(16, 923525, 503780), | |
(17, 595148, 520429), | |
(18, 177108, 572629), | |
(19, 750923, 511482), | |
(20, 440902, 532446), | |
(21, 881418, 505504), | |
(22, 422489, 534197), | |
(23, 979858, 501616), | |
(24, 685893, 514935), | |
(25, 747477, 511661), | |
(26, 167214, 575367), | |
(27, 234140, 559696), | |
(28, 940238, 503122), | |
(29, 728969, 512609), | |
(30, 232083, 560102), | |
(31, 900971, 504694), | |
(32, 688801, 514772), | |
(33, 189664, 569402), | |
(34, 891022, 505104), | |
(35, 445689, 531996), | |
(36, 119570, 591871), | |
(37, 821453, 508118), | |
(38, 371084, 539600), | |
(39, 911745, 504251), | |
(40, 623655, 518600), | |
(41, 144361, 582486), | |
(42, 352442, 541775), | |
(43, 420726, 534367), | |
(44, 295298, 549387), | |
(45, 6530, 787777), | |
(46, 468397, 529976), | |
(47, 672336, 515696), | |
(48, 431861, 533289), | |
(49, 84228, 610150), | |
(50, 805376, 508857), | |
(51, 444409, 532117), | |
(52, 33833, 663511), | |
(53, 381850, 538396), | |
(54, 402931, 536157), | |
(55, 92901, 604930), | |
(56, 304825, 548004), | |
(57, 731917, 512452), | |
(58, 753734, 511344), | |
(59, 51894, 637373), | |
(60, 151578, 580103), | |
(61, 295075, 549421), | |
(62, 303590, 548183), | |
(63, 333594, 544123), | |
(64, 683952, 515042), | |
(65, 60090, 628880), | |
(66, 951420, 502692), | |
(67, 28335, 674991), | |
(68, 714940, 513349), | |
(69, 343858, 542826), | |
(70, 549279, 523586), | |
(71, 804571, 508887), | |
(72, 260653, 554881), | |
(73, 291399, 549966), | |
(74, 402342, 536213), | |
(75, 408889, 535550), | |
(76, 40328, 652524), | |
(77, 375856, 539061), | |
(78, 768907, 510590), | |
(79, 165993, 575715), | |
(80, 976327, 501755), | |
(81, 898500, 504795), | |
(82, 360404, 540830), | |
(83, 478714, 529095), | |
(84, 694144, 514472), | |
(85, 488726, 528258), | |
(86, 841380, 507226), | |
(87, 328012, 544839), | |
(88, 22389, 690868), | |
(89, 604053, 519852), | |
(90, 329514, 544641), | |
(91, 772965, 510390), | |
(92, 492798, 527927), | |
(93, 30125, 670983), | |
(94, 895603, 504906), | |
(95, 450785, 531539), | |
(96, 840237, 507276), | |
(97, 380711, 538522), | |
(98, 63577, 625673), | |
(99, 76801, 615157), | |
(100, 502694, 527123), | |
(101, 597706, 520257), | |
(102, 310484, 547206), | |
(103, 944468, 502959), | |
(104, 121283, 591152), | |
(105, 451131, 531507), | |
(106, 566499, 522367), | |
(107, 425373, 533918), | |
(108, 40240, 652665), | |
(109, 39130, 654392), | |
(110, 714926, 513355), | |
(111, 469219, 529903), | |
(112, 806929, 508783), | |
(113, 287970, 550487), | |
(114, 92189, 605332), | |
(115, 103841, 599094), | |
(116, 671839, 515725), | |
(117, 452048, 531421), | |
(118, 987837, 501323), | |
(119, 935192, 503321), | |
(120, 88585, 607450), | |
(121, 613883, 519216), | |
(122, 144551, 582413), | |
(123, 647359, 517155), | |
(124, 213902, 563816), | |
(125, 184120, 570789), | |
(126, 258126, 555322), | |
(127, 502546, 527130), | |
(128, 407655, 535678), | |
(129, 401528, 536306), | |
(130, 477490, 529193), | |
(131, 841085, 507237), | |
(132, 732831, 512408), | |
(133, 833000, 507595), | |
(134, 904694, 504542), | |
(135, 581435, 521348), | |
(136, 455545, 531110), | |
(137, 873558, 505829), | |
(138, 94916, 603796), | |
(139, 720176, 513068), | |
(140, 545034, 523891), | |
(141, 246348, 557409), | |
(142, 556452, 523079), | |
(143, 832015, 507634), | |
(144, 173663, 573564), | |
(145, 502634, 527125), | |
(146, 250732, 556611), | |
(147, 569786, 522139), | |
(148, 216919, 563178), | |
(149, 521815, 525623), | |
(150, 92304, 605270), | |
(151, 164446, 576167), | |
(152, 753413, 511364), | |
(153, 11410, 740712), | |
(154, 448845, 531712), | |
(155, 925072, 503725), | |
(156, 564888, 522477), | |
(157, 7062, 780812), | |
(158, 641155, 517535), | |
(159, 738878, 512100), | |
(160, 636204, 517828), | |
(161, 372540, 539436), | |
(162, 443162, 532237), | |
(163, 571192, 522042), | |
(164, 655350, 516680), | |
(165, 299741, 548735), | |
(166, 581914, 521307), | |
(167, 965471, 502156), | |
(168, 513441, 526277), | |
(169, 808682, 508700), | |
(170, 237589, 559034), | |
(171, 543300, 524025), | |
(172, 804712, 508889), | |
(173, 247511, 557192), | |
(174, 543486, 524008), | |
(175, 504383, 526992), | |
(176, 326529, 545039), | |
(177, 792493, 509458), | |
(178, 86033, 609017), | |
(179, 126554, 589005), | |
(180, 579379, 521481), | |
(181, 948026, 502823), | |
(182, 404777, 535969), | |
(183, 265767, 554022), | |
(184, 266876, 553840), | |
(185, 46631, 643714), | |
(186, 492397, 527958), | |
(187, 856106, 506581), | |
(188, 795757, 509305), | |
(189, 748946, 511584), | |
(190, 294694, 549480), | |
(191, 409781, 535463), | |
(192, 775887, 510253), | |
(193, 543747, 523991), | |
(194, 210592, 564536), | |
(195, 517119, 525990), | |
(196, 520253, 525751), | |
(197, 247926, 557124), | |
(198, 592141, 520626), | |
(199, 346580, 542492), | |
(200, 544969, 523902), | |
(201, 506501, 526817), | |
(202, 244520, 557738), | |
(203, 144745, 582349), | |
(204, 69274, 620858), | |
(205, 292620, 549784), | |
(206, 926027, 503687), | |
(207, 736320, 512225), | |
(208, 515528, 526113), | |
(209, 407549, 535688), | |
(210, 848089, 506927), | |
(211, 24141, 685711), | |
(212, 9224, 757964), | |
(213, 980684, 501586), | |
(214, 175259, 573121), | |
(215, 489160, 528216), | |
(216, 878970, 505604), | |
(217, 969546, 502002), | |
(218, 525207, 525365), | |
(219, 690461, 514675), | |
(220, 156510, 578551), | |
(221, 659778, 516426), | |
(222, 468739, 529945), | |
(223, 765252, 510770), | |
(224, 76703, 615230), | |
(225, 165151, 575959), | |
(226, 29779, 671736), | |
(227, 928865, 503569), | |
(228, 577538, 521605), | |
(229, 927555, 503618), | |
(230, 185377, 570477), | |
(231, 974756, 501809), | |
(232, 800130, 509093), | |
(233, 217016, 563153), | |
(234, 365709, 540216), | |
(235, 774508, 510320), | |
(236, 588716, 520851), | |
(237, 631673, 518104), | |
(238, 954076, 502590), | |
(239, 777828, 510161), | |
(240, 990659, 501222), | |
(241, 597799, 520254), | |
(242, 786905, 509727), | |
(243, 512547, 526348), | |
(244, 756449, 511212), | |
(245, 869787, 505988), | |
(246, 653747, 516779), | |
(247, 84623, 609900), | |
(248, 839698, 507295), | |
(249, 30159, 670909), | |
(250, 797275, 509234), | |
(251, 678136, 515373), | |
(252, 897144, 504851), | |
(253, 989554, 501263), | |
(254, 413292, 535106), | |
(255, 55297, 633667), | |
(256, 788650, 509637), | |
(257, 486748, 528417), | |
(258, 150724, 580377), | |
(259, 56434, 632490), | |
(260, 77207, 614869), | |
(261, 588631, 520859), | |
(262, 611619, 519367), | |
(263, 100006, 601055), | |
(264, 528924, 525093), | |
(265, 190225, 569257), | |
(266, 851155, 506789), | |
(267, 682593, 515114), | |
(268, 613043, 519275), | |
(269, 514673, 526183), | |
(270, 877634, 505655), | |
(271, 878905, 505602), | |
(272, 1926, 914951), | |
(273, 613245, 519259), | |
(274, 152481, 579816), | |
(275, 841774, 507203), | |
(276, 71060, 619442), | |
(277, 865335, 506175), | |
(278, 90244, 606469), | |
(279, 302156, 548388), | |
(280, 399059, 536557), | |
(281, 478465, 529113), | |
(282, 558601, 522925), | |
(283, 69132, 620966), | |
(284, 267663, 553700), | |
(285, 988276, 501310), | |
(286, 378354, 538787), | |
(287, 529909, 525014), | |
(288, 161733, 576968), | |
(289, 758541, 511109), | |
(290, 823425, 508024), | |
(291, 149821, 580667), | |
(292, 269258, 553438), | |
(293, 481152, 528891), | |
(294, 120871, 591322), | |
(295, 972322, 501901), | |
(296, 981350, 501567), | |
(297, 676129, 515483), | |
(298, 950860, 502717), | |
(299, 119000, 592114), | |
(300, 392252, 537272), | |
(301, 191618, 568919), | |
(302, 946699, 502874), | |
(303, 289555, 550247), | |
(304, 799322, 509139), | |
(305, 703886, 513942), | |
(306, 194812, 568143), | |
(307, 261823, 554685), | |
(308, 203052, 566221), | |
(309, 217330, 563093), | |
(310, 734748, 512313), | |
(311, 391759, 537328), | |
(312, 807052, 508777), | |
(313, 564467, 522510), | |
(314, 59186, 629748), | |
(315, 113447, 594545), | |
(316, 518063, 525916), | |
(317, 905944, 504492), | |
(318, 613922, 519213), | |
(319, 439093, 532607), | |
(320, 445946, 531981), | |
(321, 230530, 560399), | |
(322, 297887, 549007), | |
(323, 459029, 530797), | |
(324, 403692, 536075), | |
(325, 855118, 506616), | |
(326, 963127, 502245), | |
(327, 841711, 507208), | |
(328, 407411, 535699), | |
(329, 924729, 503735), | |
(330, 914823, 504132), | |
(331, 333725, 544101), | |
(332, 176345, 572832), | |
(333, 912507, 504225), | |
(334, 411273, 535308), | |
(335, 259774, 555036), | |
(336, 632853, 518038), | |
(337, 119723, 591801), | |
(338, 163902, 576321), | |
(339, 22691, 689944), | |
(340, 402427, 536212), | |
(341, 175769, 572988), | |
(342, 837260, 507402), | |
(343, 603432, 519893), | |
(344, 313679, 546767), | |
(345, 538165, 524394), | |
(346, 549026, 523608), | |
(347, 61083, 627945), | |
(348, 898345, 504798), | |
(349, 992556, 501153), | |
(350, 369999, 539727), | |
(351, 32847, 665404), | |
(352, 891292, 505088), | |
(353, 152715, 579732), | |
(354, 824104, 507997), | |
(355, 234057, 559711), | |
(356, 730507, 512532), | |
(357, 960529, 502340), | |
(358, 388395, 537687), | |
(359, 958170, 502437), | |
(360, 57105, 631806), | |
(361, 186025, 570311), | |
(362, 993043, 501133), | |
(363, 576770, 521664), | |
(364, 215319, 563513), | |
(365, 927342, 503628), | |
(366, 521353, 525666), | |
(367, 39563, 653705), | |
(368, 752516, 511408), | |
(369, 110755, 595770), | |
(370, 309749, 547305), | |
(371, 374379, 539224), | |
(372, 919184, 503952), | |
(373, 990652, 501226), | |
(374, 647780, 517135), | |
(375, 187177, 570017), | |
(376, 168938, 574877), | |
(377, 649558, 517023), | |
(378, 278126, 552016), | |
(379, 162039, 576868), | |
(380, 658512, 516499), | |
(381, 498115, 527486), | |
(382, 896583, 504868), | |
(383, 561170, 522740), | |
(384, 747772, 511647), | |
(385, 775093, 510294), | |
(386, 652081, 516882), | |
(387, 724905, 512824), | |
(388, 499707, 527365), | |
(389, 47388, 642755), | |
(390, 646668, 517204), | |
(391, 571700, 522007), | |
(392, 180430, 571747), | |
(393, 710015, 513617), | |
(394, 435522, 532941), | |
(395, 98137, 602041), | |
(396, 759176, 511070), | |
(397, 486124, 528467), | |
(398, 526942, 525236), | |
(399, 878921, 505604), | |
(400, 408313, 535602), | |
(401, 926980, 503640), | |
(402, 882353, 505459), | |
(403, 566887, 522345), | |
(404, 3326, 853312), | |
(405, 911981, 504248), | |
(406, 416309, 534800), | |
(407, 392991, 537199), | |
(408, 622829, 518651), | |
(409, 148647, 581055), | |
(410, 496483, 527624), | |
(411, 666314, 516044), | |
(412, 48562, 641293), | |
(413, 672618, 515684), | |
(414, 443676, 532187), | |
(415, 274065, 552661), | |
(416, 265386, 554079), | |
(417, 347668, 542358), | |
(418, 31816, 667448), | |
(419, 181575, 571446), | |
(420, 961289, 502320), | |
(421, 365689, 540214), | |
(422, 987950, 501317), | |
(423, 932299, 503440), | |
(424, 27388, 677243), | |
(425, 746701, 511701), | |
(426, 492258, 527969), | |
(427, 147823, 581323), | |
(428, 57918, 630985), | |
(429, 838849, 507333), | |
(430, 678038, 515375), | |
(431, 27852, 676130), | |
(432, 850241, 506828), | |
(433, 818403, 508253), | |
(434, 131717, 587014), | |
(435, 850216, 506834), | |
(436, 904848, 504529), | |
(437, 189758, 569380), | |
(438, 392845, 537217), | |
(439, 470876, 529761), | |
(440, 925353, 503711), | |
(441, 285431, 550877), | |
(442, 454098, 531234), | |
(443, 823910, 508003), | |
(444, 318493, 546112), | |
(445, 766067, 510730), | |
(446, 261277, 554775), | |
(447, 421530, 534289), | |
(448, 694130, 514478), | |
(449, 120439, 591498), | |
(450, 213308, 563949), | |
(451, 854063, 506662), | |
(452, 365255, 540263), | |
(453, 165437, 575872), | |
(454, 662240, 516281), | |
(455, 289970, 550181), | |
(456, 847977, 506933), | |
(457, 546083, 523816), | |
(458, 413252, 535113), | |
(459, 975829, 501767), | |
(460, 361540, 540701), | |
(461, 235522, 559435), | |
(462, 224643, 561577), | |
(463, 736350, 512229), | |
(464, 328303, 544808), | |
(465, 35022, 661330), | |
(466, 307838, 547578), | |
(467, 474366, 529458), | |
(468, 873755, 505819), | |
(469, 73978, 617220), | |
(470, 827387, 507845), | |
(471, 670830, 515791), | |
(472, 326511, 545034), | |
(473, 309909, 547285), | |
(474, 400970, 536363), | |
(475, 884827, 505352), | |
(476, 718307, 513175), | |
(477, 28462, 674699), | |
(478, 599384, 520150), | |
(479, 253565, 556111), | |
(480, 284009, 551093), | |
(481, 343403, 542876), | |
(482, 446557, 531921), | |
(483, 992372, 501160), | |
(484, 961601, 502308), | |
(485, 696629, 514342), | |
(486, 919537, 503945), | |
(487, 894709, 504944), | |
(488, 892201, 505051), | |
(489, 358160, 541097), | |
(490, 448503, 531745), | |
(491, 832156, 507636), | |
(492, 920045, 503924), | |
(493, 926137, 503675), | |
(494, 416754, 534757), | |
(495, 254422, 555966), | |
(496, 92498, 605151), | |
(497, 826833, 507873), | |
(498, 660716, 516371), | |
(499, 689335, 514746), | |
(500, 160045, 577467), | |
(501, 814642, 508425), | |
(502, 969939, 501993), | |
(503, 242856, 558047), | |
(504, 76302, 615517), | |
(505, 472083, 529653), | |
(506, 587101, 520964), | |
(507, 99066, 601543), | |
(508, 498005, 527503), | |
(509, 709800, 513624), | |
(510, 708000, 513716), | |
(511, 20171, 698134), | |
(512, 285020, 550936), | |
(513, 266564, 553891), | |
(514, 981563, 501557), | |
(515, 846502, 506991), | |
(516, 334, 1190800), | |
(517, 209268, 564829), | |
(518, 9844, 752610), | |
(519, 996519, 501007), | |
(520, 410059, 535426), | |
(521, 432931, 533188), | |
(522, 848012, 506929), | |
(523, 966803, 502110), | |
(524, 983434, 501486), | |
(525, 160700, 577267), | |
(526, 504374, 526989), | |
(527, 832061, 507640), | |
(528, 392825, 537214), | |
(529, 443842, 532165), | |
(530, 440352, 532492), | |
(531, 745125, 511776), | |
(532, 13718, 726392), | |
(533, 661753, 516312), | |
(534, 70500, 619875), | |
(535, 436952, 532814), | |
(536, 424724, 533973), | |
(537, 21954, 692224), | |
(538, 262490, 554567), | |
(539, 716622, 513264), | |
(540, 907584, 504425), | |
(541, 60086, 628882), | |
(542, 837123, 507412), | |
(543, 971345, 501940), | |
(544, 947162, 502855), | |
(545, 139920, 584021), | |
(546, 68330, 621624), | |
(547, 666452, 516038), | |
(548, 731446, 512481), | |
(549, 953350, 502619), | |
(550, 183157, 571042), | |
(551, 845400, 507045), | |
(552, 651548, 516910), | |
(553, 20399, 697344), | |
(554, 861779, 506331), | |
(555, 629771, 518229), | |
(556, 801706, 509026), | |
(557, 189207, 569512), | |
(558, 737501, 512168), | |
(559, 719272, 513115), | |
(560, 479285, 529045), | |
(561, 136046, 585401), | |
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