54道"约瑟夫环"题目

王守恩

将正整数1—n围成一圈, 从1开始, 第一次固定A(奇数=拿走,偶数=留下)。之后每次B(奇数=留下,偶数=拿走),C(奇数=拿走,偶数=留下)循环模拟此过程, 直至最后剩下1个数字。则最后剩下的1个数字是_____。

题目(01)—{1, 1, 1}—拿走1, 3, 5, 7, ......
01。{1, 2, 2, 4, 2, 4, 6, 8, 2, 4, 6, 8, 10, 12, 14, 16, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56},
题目(02)—{1, 1, 1}—拿走2, 4, 6, 8, ......
02。{1, 1, 3, 1, 3, 5, 7, 1, 3, 5, 7, 9, 11, 13, 15, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57},
题目(03)—{1, 1, 2}—拿走1, 3,4, 6,7, 9,10, ......
03。{1, 2, 2, 2, 5, 5, 2, 8, 5, 2, 8, 5, 11, 8, 14, 11, 17, 14, 2, 17, 5, 20, 8, 23, 11, 26, 14, 2, 17, 5, 20, 8, 23, 11, 26, 14, 29, 17, 32, 20, 35, 23, 38, 26, 41, 29, 44, 32, 47, 35, 50, 38, 53, 41, 2, 44, 5, 47, 8, 50},
题目(04)—{1, 1, 2}—拿走2, 5, 8, 11, ......
04。{1, 1, 1, 4, 3, 6, 3, 6, 9, 3, 6, 9, 12, 1, 4, 7,10, 13, 16, 19, 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40},
题目(05)—{1, 1, 3}—拿走1, 3,4,5, 7,8,9, 11,12,13, ......
05。{1, 2, 2, 2, 2, 6, 6, 6, 2, 10, 10, 6, 2, 14, 10, 6, 2, 14, 10, 6, 18, 14, 10, 22, 18, 14, 26, 22, 18, 30, 26, 22, 2, 30, 26, 6, 34, 30, 10, 38, 34, 14, 42, 38, 18, 46, 42, 22, 2, 46, 26, 6, 50, 30, 10, 54, 34, 14, 58, 38},
题目(06)—{1, 1, 3}—拿走2, 6, 10, 14, ......
06。{1, 1, 3, 4, 4, 3, 7, 4, 8, 3, 7, 11, 3, 7, 11, 15, 3, 7, 11, 15, 19, 1, 5, 9, 13, 17, 21, 25, 29, 4, 8, 12, 16, 20, 24, 28, 32, 36, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 1, 5, 9, 13, 17, 21, 25, 29, 33},
题目(07)—{1, 2, 1}—拿走1, 4, 7, 10, ......
07。{1, 2, 3, 3, 2, 5, 2, 5, 8, 2, 5, 8, 11, 14, 3, 6, 9, 12, 15, 18, 21, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39},
题目(08)—{1, 2, 1}—拿走2,3, 5,6, 8,9, 11,12, ......
08。{1, 1, 1, 4, 4, 1, 7, 4, 1, 7, 4, 10, 7, 13, 10, 16, 13, 1, 16, 4, 19, 7, 22, 10, 25, 13, 1, 16, 4, 19, 7, 22, 10, 25, 13, 28, 16, 31, 19, 34, 22, 37, 25, 40, 28, 43, 31, 46, 34, 49, 37, 52, 40, 1, 43, 4, 46, 7, 49, 10},
题目(09)—{1, 2, 2}—拿走1, 4,5, 8,9, 12,13, ......
09。{1, 2, 3, 3, 3, 2, 7, 6, 3, 10, 7, 3, 11, 7, 15, 11, 3, 15, 7, 19, 11, 2, 15, 6, 19, 10, 23, 14, 27, 18, 31, 22, 3, 26, 7, 30, 11, 34, 15, 38, 19, 42, 23, 3, 27, 7, 31, 11, 35, 15, 39, 19, 43, 23, 47, 27, 51, 31, 55, 35},
题目(10)—{1, 2, 2}—拿走2,3, 6,7, 10,11, 14,15, ......
10。{1, 1, 1, 1, 5, 5, 4, 1, 8, 5, 1, 9, 5, 13, 9, 1, 13, 5, 17, 9, 21, 13, 4, 17, 8, 21, 12, 25, 16, 29, 20, 1, 24, 5, 28, 9, 32, 13, 36, 17, 40, 21, 1, 25, 5, 29, 9, 33, 13, 37, 17, 41, 21, 45, 25, 49, 29, 53, 33, 57},
题目(11)—{1, 2, 3}—拿走1, 4,5,6, 9,10,11, 14,15,16, ......
11。{1, 2, 3, 3, 3, 3, 2, 8, 8, 7, 3, 2, 12, 8, 7, 2, 13, 12, 7, 18, 17, 12, 23, 22, 17, 3, 27, 22, 8, 3, 27, 13, 8, 32, 18, 13, 37, 23, 18, 3, 28, 23, 8, 33, 28, 13, 38, 33, 18, 43, 38, 23, 48, 43, 28, 53, 48, 33, 58, 53},
题目(12)—{1, 2, 3}—拿走2,3, 7,8, 12,13, 17,18, ......
12。{1, 1, 1, 4, 1, 5, 6, 4, 4, 9, 9, 4, 1, 9, 6, 14, 11, 1, 16, 6, 21, 11, 5, 16, 10, 21, 15, 26, 20, 1, 25, 6, 30, 11, 35, 16, 5, 21, 10, 26, 15, 31, 20, 36, 25, 41, 30, 46, 35, 1, 40, 6, 45, 11, 50, 16, 55, 21, 1, 26},
题目(13)—{1, 3, 1}—拿走1, 5, 9, 13, ......
13。{1, 2, 2, 3, 3, 2, 6, 3, 7, 2, 6, 10, 2, 6, 10, 14, 2, 6, 10, 14, 18, 22, 4, 8, 12, 16, 20, 24, 28, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 4, 8, 12, 16, 20, 24, 28, 32},
题目(14)—{1, 3, 1}—拿走2,3,4, 6,7,8, 10,11,12, 14,15,16, ......
14。{1, 1, 1, 1, 5, 5, 5, 1, 9, 9, 5, 1, 13, 9, 5, 1, 13, 9, 5, 17, 13, 9, 21, 17, 13, 25, 21, 17, 29, 25, 21, 1, 29, 25, 5, 33, 29, 9, 37, 33, 13, 41, 37, 17, 45, 41, 21, 1, 45, 25, 5, 49, 29, 9, 53, 33, 13, 57, 37, 17},
题目(15)—{1, 3, 2}—拿走1, 5,6, 10,11, 15,16, ......
15。{1, 2, 2, 4, 3, 4, 2, 2, 7, 7, 2, 12, 7, 4, 12, 9, 17, 14, 4, 19, 9, 3, 14, 8, 19, 13, 24, 18, 29, 23, 4, 28, 9, 33, 14, 3, 19, 8, 24, 13, 29, 18, 34, 23, 39, 28, 44, 33, 49, 38, 4, 43, 9, 48, 14, 53, 19, 58, 24, 4},
题目(16)—{1, 3, 2}—拿走2,3,4, 7,8,9, 12,13,14, 17,18,19, ......
16。{1, 1, 1, 1, 1, 6, 6, 6, 5, 1, 11, 10, 6, 5, 15, 11, 10, 5, 16, 15, 10, 21, 20, 15, 1, 25, 20, 6, 1, 25, 11, 6, 30, 16, 11, 35, 21, 16, 1, 26, 21, 6, 31, 26, 11, 36, 31, 16, 41, 36, 21, 46, 41, 26, 51, 46, 31, 56, 51, 36},
题目(17)—{1, 3, 3}—拿走1, 5,6,7, 11,12,13, 17,18,19, ......
17。{1, 2, 2, 4, 4, 3, 4, 3, 9, 10, 9, 4, 4, 2, 10, 10, 8, 16, 16, 14, 2, 22, 20, 8, 4, 26, 14, 10, 4, 20, 16, 10, 26, 22, 16, 32, 28, 22, 38, 34, 28, 3, 40, 34, 9, 46, 40, 15, 4, 46, 21, 10, 52, 27, 16, 3, 33, 22, 9, 39}
题目(18)—{1, 3, 3}—拿走2,3,4, 8,9,10, 14,15,16, 20,21,22, ......
18。{1, 1, 1, 1, 5, 1, 7, 6, 7, 6, 1, 1, 12, 7, 7, 5, 13, 13, 11, 19, 19, 17, 5, 1, 23, 11, 7, 1, 17, 13, 7, 23, 19, 13, 29, 25, 19, 35, 31, 25, 41, 37, 31, 6, 43, 37, 12, 1, 43, 18, 7, 49, 24, 13, 55, 30, 19, 6, 36, 25}
题目(19)—{2, 1, 1}—拿走1,2, 4, 6, 8, ......
19。{1, 2, 3, 3, 5, 3, 5, 7, 9, 3, 5, 7, 9, 11, 13, 15, 17, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55},
题目(20)—{2, 1, 1}—拿走3, 5, 7, 9, ......
20。{1, 2, 1, 2, 4, 6, 1, 2, 4, 6, 8, 10, 12, 14, 1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58},
题目(21)—{2, 1, 2}—拿走1,2, 4,5, 7,8, 10,11, ......
21。{1, 2, 3, 3, 3, 6, 6, 3, 9, 6, 3, 9, 6, 12, 9, 15, 12, 18, 15, 3, 18, 6, 21, 9, 24, 12, 27, 15, 3, 18, 6, 21, 9, 24, 12, 27, 15, 30, 18, 33, 21, 36, 24, 39, 27, 42, 30, 45, 33, 48, 36, 51, 39, 54, 42, 3, 45, 6, 48, 9},
题目(22)—{2, 1, 2}—拿走3, 6, 9, 12, ......
22。{1, 2, 2, 1, 4, 1, 4, 7, 1, 4, 7, 10, 13, 2, 5, 8, 11, 14, 17, 20, 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41},
题目(23)—{2, 1, 3}—拿走1,2, 4,5,6, 8,9,10, 12,13,14, ......
23。{1, 2, 3, 3, 3, 3, 7, 7, 7, 3, 11, 11, 7, 3, 15, 11, 7, 3, 15, 11, 7, 19, 15, 11, 23, 19, 15, 27, 23, 19, 31, 27, 23, 3, 31, 27, 7, 35, 31, 11, 39, 35, 15, 43, 39, 19, 47, 43, 23, 3, 47, 27, 7, 51, 31, 11, 55, 35, 15, 59},
题目(24)—{2, 1, 3}—拿走3, 7, 11, 15, ......
24。{1, 2, 1, 1, 5, 4, 1, 5, 9, 4, 8, 12, 4, 8, 12, 16, 4, 8, 12, 16, 20, 2, 6, 10, 14, 18, 22, 26, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 2, 6, 10, 14, 18, 22, 26, 30, 34},
题目(25)—{2, 2, 1}—拿走1,2, 5, 8, 11, ......
25。{1, 2, 3, 4, 4, 3, 6, 3, 6, 9, 3, 6, 9, 12, 15, 4, 7, 10, 13, 16, 19, 22, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37},
题目(26)—{2, 2, 1}—拿走3,4, 6,7, 9,10, 12,13, ......
26。{1, 2, 2, 1, 5, 2, 1, 5, 2, 8, 5, 11, 8, 14, 11, 1, 14, 2, 17, 5, 20, 8, 23, 11, 1, 14, 2, 17, 5, 20, 8, 23, 11, 26, 14, 29, 17, 32, 20, 35, 23, 38, 26, 41, 29, 44, 32, 47, 35, 50, 38, 1, 41, 2, 44, 5, 47, 8, 50, 11},
题目(27)—{2, 2, 2}—拿走1,2, 5,6, 9,10, 13,14, ......
27。{1, 2, 3, 4, 4, 4, 3, 8, 7, 4, 11, 8, 4, 12, 8, 16, 12, 4, 16, 8, 20, 12, 3, 16, 7, 20, 11, 24, 15, 28, 19, 32, 23, 4, 27, 8, 31, 12, 35, 16, 39, 20, 43, 24, 4, 28, 8, 32, 12, 36, 16, 40, 20, 44, 24, 48, 28, 52, 32, 56},
题目(28)—{2, 2, 2}—拿走3,4, 7,8, 11,12, 15,16, ......
28。{1, 2, 2, 2, 1, 6, 5, 2, 9, 6, 2, 10, 6, 14, 10, 2, 14, 6, 18, 10, 1, 14, 5, 18, 9, 22, 13, 26, 17, 30, 21, 2, 25, 6, 29, 10, 33, 14, 37, 18, 41, 22, 2, 26, 6, 30, 10, 34, 14, 38, 18, 42, 22, 46, 26, 50, 30, 54, 34, 58},
题目(29)—{2, 2, 3}—拿走1,2, 5,6,7, 10,11,12, 15,16,17, ......
29。{1, 2, 3, 4, 4, 4, 4, 3, 9, 9, 8, 4, 3, 13, 9, 8, 3, 14, 13, 8, 19, 18, 13, 24, 23, 18, 4, 28, 23, 9, 4, 28, 14, 9, 33, 19, 14, 38, 24, 19, 4, 29, 24, 9, 34, 29, 14, 39, 34, 19, 44, 39, 24, 49, 44, 29, 54, 49, 34, 59},
题目(30)—{2, 2, 3}—拿走3,4, 8,9, 13,14, 18,19, ......
30。{1, 2, 2, 1, 2, 6, 7, 5, 5, 10, 10, 5, 2, 10, 7, 15, 12, 2, 17, 7, 1, 12, 6, 17, 11, 22, 16, 27, 21, 2, 26, 7, 31, 12, 1, 17, 6, 22, 11, 27, 16, 32, 21, 37, 26, 42, 31, 47, 36, 2, 41, 7, 46, 12, 51, 17, 56, 22, 2, 27},
题目(31)—{2, 3, 1}—拿走1,2, 6, 10, 14, ......
31。{1, 2, 3, 3, 4, 4, 3, 7, 4, 8, 3, 7, 11, 3, 7, 11, 15, 3, 7, 11, 15, 19, 23, 5, 9, 13, 17, 21, 25, 29, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 5, 9, 13, 17, 21, 25, 29},
题目(32)—{2, 3, 1}—拿走3,4,5, 7,8,9, 11,12,13, 15,16,17, ......
32。{1, 2, 2, 2, 1, 6, 6, 2, 1, 10, 6, 2, 1, 10, 6, 2, 14, 10, 6, 18, 14, 10, 22, 18, 14, 26, 22, 18, 1, 26, 22, 2, 30, 26, 6, 34, 30, 10, 38, 34, 14, 42, 38, 18, 1, 42, 22, 2, 46, 26, 6, 50, 30, 10, 54, 34, 14, 58, 38, 18},
题目(33)—{2, 3, 2}—拿走1,2, 6,7, 11,12, 16,17, ......
33。{1, 2, 3, 3, 5, 4, 5, 3, 3, 8, 8, 3, 13, 8, 5, 13, 10, 18, 15, 5, 20, 10, 4, 15, 9, 20, 14, 25, 19, 30, 24, 5, 29, 10, 34, 15, 4, 20, 9, 25, 14, 30, 19, 35, 24, 40, 29, 45, 34, 50, 39, 5, 44, 10, 49, 15, 54, 20, 59, 25},
题目(34)—{2, 3, 2}—拿走3,4,5, 8,9,10, 13,14,15, 18,19,20, ......
34。{1, 2, 2, 2, 2, 1, 7, 7, 6, 2, 1, 11, 7, 6, 1, 12, 11, 6, 17, 16, 11, 22, 21, 16, 2, 26, 21, 7, 2, 26, 12, 7, 31, 17, 12, 36, 22, 17, 2, 27, 22, 7, 32, 27, 12, 37, 32, 17, 42, 37, 22, 47, 42, 27, 52, 47, 32, 57, 52, 37},
题目(35)—{2, 3, 3}—拿走1,2, 6,7,8, 12,13,14, 18,19,20, ......
35。{1, 2, 3, 3, 5, 5, 4, 5, 4, 10, 11, 10, 5, 5, 3, 11, 11, 9, 17, 17, 15, 3, 23, 21, 9, 5, 27, 15, 11, 5, 21, 17, 11, 27, 23, 17, 33, 29, 23, 39, 35, 29, 4, 41, 35, 10, 47, 41, 16, 5, 47, 22, 11, 53, 28, 17, 4, 34, 23, 10}
题目(36)—{2, 3, 3}—拿走3,4,5, 9,10,11, 15,16,17, 21,22,23, ......
36。{1, 2, 2, 2, 1, 2, 1, 7, 8, 7, 2, 2, 13, 8, 8, 6, 14, 14, 12, 20, 20, 18, 6, 2, 24, 12, 8, 2, 18, 14, 8, 24, 20, 14, 30, 26, 20, 36, 32, 26, 1, 38, 32, 7, 44, 38, 13, 2, 44, 19, 8, 50, 25, 14, 1, 31, 20, 7, 37, 26}
题目(37)—{3, 1, 1}—拿走1,2,3, 5, 7, 9, ......
37。{1, 2, 3, 4, 4, 6, 4, 6, 8, 10, 4, 6, 8, 10, 12, 14, 16, 18, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54},
题目(38)—{3, 1, 1}—拿走4, 6, 8, 10, ......
38。{1, 1, 2, 3, 5, 1, 2, 3, 5, 7, 9, 11, 13, 1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59},
题目(39)—{3, 1, 2}—拿走1,2,3, 5,6, 8,9, 11,12, ......
39。{1, 2, 3, 4, 4, 4, 7, 7, 4, 10, 7, 4, 10, 7, 13, 10, 16, 13, 19, 16, 4, 19, 7, 22, 10, 25, 13, 28, 16, 4, 19, 7, 22, 10, 25, 13, 28, 16, 31, 19, 34, 22, 37, 25, 40, 28, 43, 31, 46, 34, 49, 37, 52, 40, 55, 43, 4, 46, 7, 49},
题目(40)—{3, 1, 2}—拿走4, 7, 10, 13, ......
40。{1, 1, 3, 2, 5, 2, 5, 8, 2, 5, 8, 11, 1, 3, 6, 9, 12, 15, 18, 1, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 1, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42},
题目(41)—{3, 1, 3}—拿走1,2,3, 5,6,7, 9,10,11, 13,14,15, ......
41。{1, 2, 3, 4, 4, 4, 4, 8, 8, 8, 4, 12, 12, 8, 4, 16, 12, 8, 4, 16, 12, 8, 20, 16, 12, 24, 20, 16, 28, 24, 20, 32, 28, 24, 4, 32, 28, 8, 36, 32, 12, 40, 36, 16, 44, 40, 20, 48, 44, 24, 4, 48, 28, 8, 52, 32, 12, 56, 36, 16},
题目(42)—{3, 1, 3}—拿走4, 8, 12, 16, ......
42。{1, 1, 2, 2, 1, 5, 2, 6, 1, 5, 9, 1, 5, 9, 13, 1, 5, 9, 13, 17, 21, 3, 7, 11, 15, 19, 23, 27, 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 3, 7, 11, 15, 19, 23, 27, 31, 35},
题目(43)—{3, 2, 1}—拿走1,2,3, 6, 9, 12, ......
43。{1, 2, 3, 4, 5, 5, 4, 7, 4, 7, 10, 4, 7, 10, 13, 16, 5, 8, 11, 14, 17, 20, 23, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35},
题目(44)—{3, 2, 1}—拿走4,5, 7,8, 10,11, 13,14, ......
44。{1, 1, 3, 2, 1, 3, 2, 6, 3, 9, 6, 12, 9, 1, 12, 2, 15, 3, 18, 6, 21, 9, 1, 12, 2, 15, 3, 18, 6, 21, 9, 24, 12, 27, 15, 30, 18, 33, 21, 36, 24, 39, 27, 42, 30, 45, 33, 48, 36, 1, 39, 2, 42, 3, 45, 6, 48, 9, 51, 12},
题目(45)—{3, 2, 2}—拿走1,2,3, 6,7, 10,11, 14,15, ......
45。{1, 2, 3, 4, 5, 5, 5, 4, 9, 8, 5, 12, 9, 5, 13, 9, 17, 13, 5, 17, 9, 21, 13, 4, 17, 8, 21, 12, 25, 16, 29, 20, 33, 24, 5, 28, 9, 32, 13, 36, 17, 40, 21, 44, 25, 5, 29, 9, 33, 13, 37, 17, 41, 21, 45, 25, 49, 29, 53, 33},
题目(46)—{3, 2, 2}—拿走4,5, 8,9, 12,13, 16,17, ......
46。{1, 1, 3, 3, 2, 1, 6, 3, 1, 7, 3, 11, 7, 1, 11, 3, 15, 7, 19, 11, 2, 15, 6, 19, 10, 23, 14, 27, 18, 1, 22, 3, 26, 7, 30, 11, 34, 15, 38, 19, 1, 23, 3, 27, 7, 31, 11, 35, 15, 39, 19, 43, 23, 47, 27, 51, 31, 55, 35, 59},
题目(47)—{3, 2, 3}—拿走1,2,3, 6,7,8, 11,12,13, 16,17,18, ......
47。{1, 2, 3, 4, 5, 5, 5, 5, 4, 10, 10, 9, 5, 4, 14, 10, 9, 4, 15, 14, 9, 20, 19, 14, 25, 24, 19, 5, 29, 24, 10, 5, 29, 15, 10, 34, 20, 15, 39, 25, 20, 5, 30, 25, 10, 35, 30, 15, 40, 35, 20, 45, 40, 25, 50, 45, 30, 55, 50, 35},
题目(48)—{3, 2, 3}—拿走4,5, 9,10, 14,15, 19,20, ......
48。{1, 1, 3, 2, 3, 1, 1, 6, 6, 1, 11, 6, 3, 11, 8, 16, 13, 3, 18, 8, 2, 13, 7, 18, 12, 23, 17, 28, 22, 3, 27,  8, 32, 13, 2, 18, 7, 23, 12, 28, 17, 33, 22, 38, 27, 43, 32, 48, 37, 3, 42, 8, 47, 13, 52, 18, 57, 23, 3, 28},
题目(49)—{3, 3, 1}—拿走1,2,3, 7, 11, 15, ......
49。{1, 2, 3, 4, 4, 5, 5, 4, 8, 5, 9, 4, 8, 12, 4, 8, 12, 16, 4, 8, 12, 16, 20, 24, 6, 10, 14, 18, 22, 26, 30, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 6, 10, 14, 18, 22, 26},
题目(50)—{3, 3, 1}—拿走4,5,6, 8,9,10, 12,13,14, 16,17,18, ......
50。{1, 1, 3, 3, 2, 1, 7, 3, 2, 1, 7, 3, 2, 11, 7, 3, 15, 11, 7, 19, 15, 11, 23, 19, 15, 1, 23, 19, 2, 27, 23, 3, 31, 27, 7, 35, 31, 11, 39, 35, 15, 1, 39, 19, 2, 43, 23, 3, 47, 27, 7, 51, 31, 11, 55, 35, 15, 1, 39, 19},
题目(51)—{3, 3, 2}—拿走1,2,3, 7,8, 12,13, 17,18, ......
51。{1, 2, 3, 4, 4, 6, 5, 6, 4, 4, 9, 9, 4, 14, 9, 6, 14, 11, 19, 16, 6, 21, 11, 5, 16, 10, 21, 15, 26, 20, 31, 25, 6, 30, 11, 35, 16, 5, 21, 10, 26, 15, 31, 20, 36, 25, 41, 30, 46, 35, 51, 40, 6, 45, 11, 50, 16, 55, 21, 60},
题目(52)—{3, 3, 2}—拿走4,5,6, 9,10,11, 14,15,16, 19,20,21, ......
52。{1, 1, 3, 3, 3, 2, 1, 8, 7, 3, 2, 12, 8, 7, 2, 13, 12, 7, 18, 17, 12, 1, 22, 17, 3, 1, 22, 8, 3, 27, 13, 8, 32, 18, 13, 1, 23, 18, 3, 28, 23, 8, 33, 28, 13, 38, 33, 18, 43, 38, 23, 48, 43, 28, 53, 48, 33, 58, 53, 38},
题目(53)—{3, 3, 3}—拿走1,2,3, 7,8,9, 13,14,15, 19,20,21, ......
53。{1, 2, 3, 4, 4, 6, 6, 5, 6, 5, 11, 12, 11, 6, 6, 4, 12, 12, 10, 18, 18, 16, 4, 24, 22, 10, 6, 28, 16, 12, 6, 22, 18, 12, 28, 24, 18, 34, 30, 24, 40, 36, 30, 5, 42, 36, 11, 48, 42, 17, 6, 48, 23, 12, 54, 29, 18, 5, 35, 24}
题目(54)—{3, 3, 3}—拿走4,5,6, 10,11,12, 16,17,18, 22,23,24, ......
54。{1, 1, 3, 3, 2, 3, 2, 8, 9, 8, 3, 3, 1, 9, 9, 7, 15, 15, 13, 1, 21, 19, 7, 3, 25, 13, 9, 3, 19, 15, 9, 25, 21, 15, 31, 27, 21, 37, 33, 27, 2, 39, 33, 8, 45, 39, 14, 3, 45, 20, 9, 51, 26, 15, 2, 32, 21, 8, 38, 27}