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600 個人站一排,每次隨機殺掉一個奇數位的人,幾號最安全?

2018-07-01心靈

一開始憑直覺我選2,因為選2的話,只要1不死,你就不可能死,因為你一直是偶數,而排在隊尾的人會不斷變化奇偶,一直有死亡的風險...

然後我就寫程式碼模擬了一下,測試了十萬次,看幾號活下來的次數最多,結果如下:

前面是號碼,後面是活下來的次數。

[(597, 359), (576, 355), (598, 354), (586, 352), (587, 348), (573, 347), (578, 347), (600, 346), (560, 337), (565, 337), (585, 335), (589, 335), (583, 334), (554, 333), (564, 333), (595, 333), (577, 332), (580, 332), (596, 332), (592, 331), (599, 325), (563, 324), (568, 324), (591, 324), (562, 323), (574, 322), (546, 321), (550, 319), (551, 318), (579, 318), (567, 317), (581, 316), (584, 316), (588, 316), (557, 315), (558, 315), (522, 314), (570, 314), (566, 313), (532, 312), (548, 312), (582, 312), (547, 311), (524, 310), (525, 310), (552, 310), (555, 310), (514, 309), (559, 309), (541, 308), (507, 307), (571, 306), (515, 305), (504, 304), (527, 304), (517, 302), (538, 302), (509, 301), (518, 301), (526, 301), (553, 301), (544, 300), (542, 299), (561, 299), (520, 298), (569, 298), (536, 297), (572, 297), (492, 296), (543, 296), (516, 295), (471, 294), (497, 294), (590, 294), (594, 294), (510, 293), (528, 293), (530, 293), (549, 292), (593, 292), (485, 291), (511, 291), (470, 290), (534, 290), (540, 290), (512, 289), (496, 286), (529, 286), (513, 285), (539, 285), (556, 285), (535, 283), (483, 281), (490, 281), (506, 281), (508, 281), (533, 281), (489, 279), (457, 278), (521, 278), (545, 278), (450, 277), (479, 277), (519, 277), (523, 277), (449, 276), (495, 276), (503, 275), (537, 275), (438, 273), (494, 273), (475, 272), (531, 272), (491, 271), (502, 271), (481, 270), (501, 270), (476, 269), (477, 269), (575, 269), (484, 267), (493, 267), (417, 264), (478, 264), (432, 263), (458, 263), (498, 263), (499, 263), (452, 262), (482, 262), (460, 261), (466, 261), (486, 261), (505, 261), (454, 260), (473, 259), (440, 258), (469, 258), (443, 257), (468, 257), (451, 256), (488, 256), (409, 255), (447, 255), (422, 251), (465, 251), (436, 250), (442, 250), (385, 249), (474, 249), (480, 249), (403, 248), (406, 248), (429, 248), (472, 248), (424, 247), (448, 247), (456, 247), (462, 246), (467, 246), (384, 245), (386, 245), (416, 245), (464, 245), (431, 244), (453, 243), (500, 243), (401, 242), (463, 242), (415, 241), (445, 241), (420, 240), (414, 239), (411, 238), (444, 238), (461, 238), (412, 237), (427, 237), (446, 237), (455, 237), (399, 236), (433, 235), (435, 234), (392, 232), (423, 232), (425, 232), (459, 232), (372, 231), (419, 231), (434, 231), (387, 229), (437, 229), (404, 228), (421, 228), (487, 228), (428, 227), (439, 227), (375, 226), (398, 226), (405, 226), (391, 225), (441, 225), (389, 223), (396, 223), (377, 222), (383, 222), (366, 220), (430, 220), (347, 219), (350, 217), (341, 216), (364, 216), (382, 216), (395, 216), (407, 216), (408, 216), (357, 215), (380, 215), (390, 214), (332, 213), (367, 213), (368, 211), (410, 211), (370, 210), (374, 210), (324, 209), (426, 208), (314, 207), (358, 207), (376, 206), (381, 205), (413, 205), (361, 204), (397, 203), (349, 202), (379, 202), (402, 202), (400, 200), (343, 199), (353, 199), (362, 198), (316, 197), (371, 197), (290, 196), (356, 196), (360, 195), (373, 195), (393, 195), (388, 194), (394, 194), (418, 194), (328, 192), (345, 192), (333, 191), (344, 191), (378, 191), (325, 190), (289, 189), (327, 189), (335, 189), (340, 189), (352, 189), (354, 189), (355, 189), (319, 186), (322, 186), (326, 186), (334, 186), (329, 185), (348, 185), (287, 184), (338, 184), (369, 183), (309, 181), (320, 181), (321, 181), (301, 180), (330, 180), (346, 180), (365, 180), (311, 179), (315, 179), (268, 178), (293, 178), (363, 178), (331, 177), (272, 176), (298, 175), (342, 175), (339, 173), (302, 172), (305, 172), (359, 170), (303, 169), (308, 169), (318, 169), (288, 168), (295, 168), (274, 167), (312, 167), (286, 166), (299, 166), (336, 166), (292, 165), (310, 164), (313, 164), (351, 163), (256, 162), (294, 162), (232, 161), (276, 160), (306, 160), (291, 159), (317, 158), (337, 158), (262, 157), (278, 157), (283, 156), (300, 156), (304, 156), (323, 154), (264, 153), (270, 152), (275, 152), (296, 152), (265, 151), (282, 151), (277, 150), (307, 149), (273, 148), (279, 148), (238, 147), (263, 147), (237, 146), (261, 145), (281, 144), (297, 144), (244, 143), (255, 143), (247, 142), (248, 142), (249, 142), (267, 142), (218, 141), (280, 141), (254, 140), (266, 140), (271, 139), (284, 139), (191, 138), (240, 138), (258, 138), (211, 136), (241, 136), (253, 136), (239, 135), (235, 133), (246, 133), (245, 132), (213, 131), (242, 131), (257, 130), (190, 129), (217, 129), (250, 129), (260, 129), (269, 128), (285, 128), (231, 127), (233, 127), (197, 126), (220, 126), (223, 125), (224, 125), (226, 125), (228, 124), (252, 124), (221, 123), (207, 122), (215, 122), (216, 121), (227, 121), (210, 120), (193, 119), (225, 119), (230, 119), (251, 119), (234, 118), (236, 118), (195, 117), (208, 117), (196, 116), (199, 116), (259, 116), (219, 115), (229, 114), (243, 113), (203, 112), (200, 111), (212, 110), (222, 108), (163, 105), (204, 105), (175, 104), (184, 104), (202, 104), (156, 102), (189, 102), (206, 102), (209, 102), (214, 102), (188, 101), (192, 99), (194, 99), (150, 98), (177, 98), (167, 97), (181, 97), (183, 95), (186, 95), (140, 94), (168, 93), (187, 93), (205, 93), (176, 92), (173, 91), (160, 90), (169, 90), (171, 90), (178, 90), (201, 90), (172, 89), (174, 89), (198, 89), (185, 88), (164, 87), (182, 87), (158, 86), (141, 85), (149, 85), (134, 83), (161, 83), (179, 83), (127, 82), (180, 82), (157, 81), (159, 81), (165, 81), (170, 81), (145, 80), (147, 80), (162, 80), (139, 79), (155, 79), (115, 78), (142, 78), (130, 77), (152, 76), (126, 75), (131, 75), (137, 75), (146, 75), (122, 74), (133, 74), (148, 73), (154, 73), (153, 72), (151, 71), (166, 71), (120, 70), (129, 70), (118, 69), (135, 69), (119, 68), (143, 67), (144, 67), (109, 66), (124, 66), (132, 66), (138, 66), (114, 65), (110, 64), (111, 63), (113, 63), (116, 63), (136, 62), (104, 61), (100, 60), (91, 59), (98, 59), (103, 59), (121, 59), (123, 59), (128, 58), (107, 57), (112, 57), (95, 56), (105, 56), (125, 56), (97, 54), (78, 53), (99, 53), (89, 52), (88, 51), (94, 51), (96, 51), (106, 49), (117, 49), (79, 48), (108, 47), (102, 46), (69, 45), (73, 45), (80, 43), (85, 43), (86, 43), (92, 43), (59, 41), (81, 41), (74, 40), (93, 40), (101, 40), (72, 39), (75, 39), (84, 39), (87, 39), (90, 39), (58, 38), (64, 38), (70, 38), (51, 37), (68, 37), (76, 36), (82, 36), (48, 35), (65, 35), (41, 34), (40, 33), (56, 33), (61, 33), (49, 32), (62, 32), (71, 32), (83, 32), (46, 31), (67, 31), (77, 31), (55, 30), (60, 30), (52, 29), (63, 29), (57, 28), (45, 27), (47, 27), (50, 27), (54, 27), (66, 27), (53, 25), (39, 23), (44, 23), (37, 22), (38, 22), (33, 21), (34, 21), (36, 21), (42, 21), (43, 21), (27, 18), (28, 18), (22, 17), (26, 16), (35, 16), (24, 15), (30, 14), (31, 14), (18, 13), (20, 13), (16, 12), (17, 12), (32, 12), (19, 11), (29, 11), (15, 10), (11, 9), (25, 9), (8, 7), (12, 7), (14, 7), (21, 7), (23, 7), (13, 6), (7, 5), (9, 5), (10, 4), (6, 3), (5, 2), (3, 1), (4, 1), (1, 0), (2, 0)]

可以看出有點反直覺,號碼越大活下來的次數越多,2反而一次都沒有幸存過...講道理2應該是有機會的,若且唯若1號和2號是最後兩個幸運兒的情況下,2號能活到最後;只要前面1死了,2必死,因為2號變成奇數了,且永遠是奇數...

然後我又換了一個思路,不是找出最後一個活下來的人,而是找每個位置被幹掉時的平均輪次,期望最大的位置就是在"殺死X人後就停止遊戲"模式下,最該選的位置。這種情況下,2才是最優解,10W次平均下來可以活334輪。

[(2, 334.85462), (4, 324.15324), (6, 318.03607), (8, 314.53773), (10, 312.15009), (12, 310.24678), (14, 309.83584), (16, 308.15376), (20, 308.08513), (24, 306.97496), (22, 306.91657), (18, 306.56934), (26, 305.27079), (34, 305.20893), (30, 305.12727), (28, 304.86014), (38, 304.68987), (36, 304.61869), (40, 304.20346), (60, 304.09304), (72, 304.05492), (46, 304.00212), (48, 303.77202), (56, 303.73308), (32, 303.70517), (68, 303.44412), (44, 303.40699), (76, 303.28368), (54, 303.27495), (58, 303.27351), (136, 303.22399), (52, 303.18093), (64, 303.16217), (92, 303.15471), (88, 303.12217), (94, 302.9876), (106, 302.94762), (74, 302.91037), (50, 302.88765), (356, 302.88328), (42, 302.83717), (102, 302.83614), (62, 302.81658), (124, 302.79908), (208, 302.6461), (100, 302.63596), (80, 302.58573), (146, 302.53383), (128, 302.40043), (182, 302.37766), (66, 302.37435), (340, 302.34032), (84, 302.31475), (78, 302.31181), (206, 302.29824), (70, 302.2765), (150, 302.26535), (108, 302.25733), (236, 302.2203), (116, 302.20057), (188, 302.185), (186, 302.17129), (126, 302.16539), (272, 302.14484), (408, 302.12267), (138, 302.0991), (282, 302.09234), (104, 302.08849), (202, 302.08609), (130, 302.05452), (454, 302.04717), (230, 302.03887), (260, 302.0247), (196, 302.01771), (348, 302.00776), (270, 302.00579), (110, 301.9752), (496, 301.9628), (90, 301.96193), (120, 301.95368), (192, 301.93925), (244, 301.93474), (468, 301.93351), (597, 301.92656), (536, 301.90763), (564, 301.90078), (416, 301.8996), (228, 301.89672), (118, 301.86935), (98, 301.86074), (220, 301.85789), (504, 301.84736), (506, 301.84461), (164, 301.83767), (82, 301.83346), (592, 301.81593), (172, 301.77913), (112, 301.77641), (160, 301.77316), (166, 301.74413), (414, 301.72875), (144, 301.72661), (156, 301.70811), (132, 301.70281), (86, 301.68918), (96, 301.68302), (342, 301.67392), (530, 301.67366), (224, 301.66795), (404, 301.66377), (152, 301.65855), (218, 301.65), (190, 301.64822), (378, 301.64469), (440, 301.64003), (276, 301.61927), (533, 301.61603), (238, 301.61226), (392, 301.59841), (596, 301.57546), (168, 301.57143), (546, 301.56303), (538, 301.55457), (248, 301.55388), (410, 301.55265), (411, 301.55163), (444, 301.53787), (364, 301.52839), (178, 301.52693), (302, 301.52463), (520, 301.52462), (290, 301.52014), (266, 301.50517), (434, 301.50079), (354, 301.49918), (422, 301.46459), (114, 301.46379), (540, 301.45644), (344, 301.45233), (306, 301.44755), (194, 301.44695), (162, 301.44612), (268, 301.44602), (365, 301.43923), (586, 301.43489), (517, 301.43298), (300, 301.43164), (296, 301.42878), (358, 301.42858), (148, 301.42713), (544, 301.4258), (522, 301.42288), (559, 301.41682), (284, 301.41189), (226, 301.41026), (245, 301.40577), (170, 301.40057), (502, 301.39821), (255, 301.3975), (396, 301.38399), (332, 301.37851), (395, 301.37768), (330, 301.36072), (334, 301.35544), (232, 301.34294), (320, 301.34237), (280, 301.34097), (198, 301.33406), (254, 301.3305), (294, 301.32553), (122, 301.31871), (438, 301.31805), (584, 301.31456), (242, 301.31203), (355, 301.30953), (516, 301.3093), (557, 301.30846), (214, 301.30454), (560, 301.30396), (367, 301.29951), (316, 301.29472), (451, 301.29425), (570, 301.29393), (500, 301.29097), (420, 301.28634), (590, 301.28286), (368, 301.27778), (324, 301.27618), (328, 301.27546), (574, 301.26491), (140, 301.25926), (134, 301.2452), (292, 301.23012), (336, 301.22657), (585, 301.2259), (389, 301.21997), (382, 301.21696), (154, 301.2139), (484, 301.21227), (448, 301.20634), (158, 301.19844), (258, 301.18464), (200, 301.18353), (209, 301.18135), (402, 301.18134), (431, 301.18078), (413, 301.1788), (433, 301.17544), (400, 301.17209), (541, 301.15425), (318, 301.154), (418, 301.15282), (486, 301.15154), (531, 301.14597), (216, 301.13614), (554, 301.13358), (142, 301.12922), (321, 301.12583), (212, 301.11879), (390, 301.10947), (436, 301.10221), (511, 301.10068), (494, 301.09707), (250, 301.09331), (518, 301.08564), (534, 301.08267), (361, 301.08264), (478, 301.08014), (394, 301.07468), (370, 301.06988), (460, 301.06917), (210, 301.06875), (376, 301.06304), (308, 301.05279), (446, 301.05051), (333, 301.04586), (412, 301.03631), (598, 301.03513), (563, 301.03156), (476, 301.02515), (338, 301.02069), (437, 301.01551), (293, 301.01252), (526, 301.00239), (452, 300.9889), (319, 300.98299), (491, 300.97416), (543, 300.96583), (213, 300.95534), (426, 300.95481), (524, 300.95458), (514, 300.94796), (331, 300.94793), (277, 300.94549), (532, 300.943), (415, 300.93183), (492, 300.92734), (303, 300.92573), (222, 300.91827), (582, 300.91764), (589, 300.91628), (346, 300.91307), (398, 300.90946), (561, 300.90728), (456, 300.90014), (473, 300.8869), (269, 300.87927), (594, 300.87904), (366, 300.86993), (278, 300.8503), (385, 300.85025), (499, 300.84888), (204, 300.84674), (295, 300.84209), (581, 300.84142), (335, 300.84045), (240, 300.83815), (443, 300.83061), (191, 300.82292), (469, 300.81836), (479, 300.80903), (464, 300.79993), (472, 300.7917), (264, 300.78885), (322, 300.77927), (428, 300.77142), (483, 300.76892), (545, 300.76889), (474, 300.76517), (558, 300.76212), (314, 300.76016), (509, 300.75938), (515, 300.75781), (176, 300.75518), (271, 300.74916), (482, 300.74316), (508, 300.73768), (566, 300.73678), (234, 300.73599), (391, 300.73318), (562, 300.73216), (591, 300.73121), (362, 300.72655), (384, 300.72311), (576, 300.71459), (430, 300.71153), (305, 300.71115), (184, 300.70853), (593, 300.70736), (447, 300.69003), (288, 300.68323), (573, 300.68065), (381, 300.67603), (547, 300.67531), (449, 300.67492), (231, 300.66485), (363, 300.65597), (180, 300.65275), (461, 300.65101), (357, 300.64421), (553, 300.63929), (374, 300.63756), (252, 300.6323), (372, 300.63123), (439, 300.62922), (599, 300.6264), (588, 300.62502), (343, 300.62028), (466, 300.61701), (253, 300.61201), (442, 300.60987), (583, 300.60926), (195, 300.6068), (137, 300.60063), (326, 300.5997), (291, 300.58589), (345, 300.58361), (174, 300.58266), (380, 300.57932), (388, 300.57581), (155, 300.57217), (490, 300.56931), (550, 300.56738), (256, 300.56594), (595, 300.55435), (298, 300.55192), (251, 300.54332), (279, 300.53939), (350, 300.53105), (397, 300.52598), (568, 300.51707), (327, 300.51672), (221, 300.50989), (312, 300.50501), (481, 300.50204), (246, 300.49963), (470, 300.49424), (274, 300.49282), (175, 300.49146), (493, 300.48546), (262, 300.48466), (432, 300.48236), (580, 300.48222), (425, 300.47463), (498, 300.47326), (205, 300.46869), (406, 300.4636), (552, 300.46066), (463, 300.45809), (459, 300.45588), (556, 300.4549), (488, 300.45307), (471, 300.45128), (360, 300.44997), (199, 300.44032), (371, 300.43315), (310, 300.43292), (485, 300.42953), (261, 300.42819), (197, 300.42151), (373, 300.41495), (229, 300.41198), (549, 300.41091), (179, 300.40888), (424, 300.40664), (267, 300.40607), (501, 300.39616), (419, 300.39156), (505, 300.39052), (578, 300.38601), (352, 300.3855), (457, 300.38335), (525, 300.37539), (542, 300.37402), (587, 300.36838), (551, 300.36684), (219, 300.35185), (329, 300.34586), (287, 300.31599), (393, 300.31475), (572, 300.30156), (503, 300.29912), (462, 300.29822), (225, 300.29569), (401, 300.29498), (453, 300.28758), (286, 300.28053), (565, 300.27658), (487, 300.27087), (510, 300.26524), (215, 300.25942), (187, 300.24968), (325, 300.24773), (407, 300.24371), (455, 300.24088), (309, 300.24075), (435, 300.2252), (512, 300.21649), (480, 300.20573), (121, 300.20046), (263, 300.19342), (353, 300.17889), (281, 300.17533), (313, 300.16192), (337, 300.1587), (301, 300.15462), (528, 300.14869), (421, 300.14814), (257, 300.14513), (265, 300.14151), (445, 300.13972), (507, 300.12832), (185, 300.12465), (495, 300.12329), (579, 300.12283), (529, 300.11603), (386, 300.11102), (151, 300.10925), (147, 300.109), (283, 300.10339), (387, 300.09651), (519, 300.09216), (243, 300.08065), (441, 300.07654), (539, 300.07124), (304, 300.07028), (349, 300.06374), (317, 300.06314), 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