连锁反应
Chain Reaction
题目详情
写下 1 到 100 之间的整数链，不重复，这样 如果 x 和 y 是链中的连续数字，则 x 整除 y 或 y 整除 x。这是长度为 12 的此类链的示例：
37、74、2、8、4、16、48、6、3、9、27、81
你能找到的最长的链是多少？
Write down a chain of integers between 1 and 100, with no repetition, such that if x and y are consecutive numbers in the chain, then x evenly divides y or y evenly divides x. Here is an example of such a chain, with length 12:
37, 74, 2, 8, 4, 16, 48, 6, 3, 9, 27, 81
What is the longest chain you can find?
解析
本月困难的开放式谜题！许多人都接近，但我们收到了 7 提交的链长度为 77，这也是我们能找到的最长的。 恭喜亚历山大·查佩尔（Alexander Chappell），七人之一，以及本月的随机 选出了 Jane Street T 恤的获胜者！他的提交是： 69 23 46 92 4 76 38 19 95 5 85 17 68 34 2 62 31 93 3 87 29 58 1 49 98 14 56 28 84 42 21 63 9 81 27 54 18 72 36 12 6 66 33 99 11 22 44 88 8 24 48 96 32 64 16 80 40 20 60 30 90 45 15 75 25 100 50 10 70 35 7 91 13 39 78 26 52
Original Explanation
Tough, open-ended puzzle this month! Many came close, but we received 7 submissions with chains of length 77, which is also the longest we could find. Congratulations to Alexander Chappell, one of the 7, and this month’s randomly chosen winner of a Jane Street t-shirt! His submission was: 69 23 46 92 4 76 38 19 95 5 85 17 68 34 2 62 31 93 3 87 29 58 1 49 98 14 56 28 84 42 21 63 9 81 27 54 18 72 36 12 6 66 33 99 11 22 44 88 8 24 48 96 32 64 16 80 40 20 60 30 90 45 15 75 25 100 50 10 70 35 7 91 13 39 78 26 52