HMMT 十一月 2013 · 冲刺赛 · 第 11 题

英文解析

11. [ 8 ] David has a unit triangular array of 10 points, 4 on each side. A looping path is a sequence
    A , A , . . . , A containing each of the 10 points exactly once, such that A and A are adjacent
    1 2 10 i i +1
    (exactly 1 unit apart) for i = 1 , 2 , . . . , 10. (Here A = A .) Find the number of looping paths in this
    11 1
    array.
    Answer: 60 There are 10 · 2 times as many loop sequences as loops. To count the number ofloops, first focus on the three corners of the array: their edges are uniquely determined. It’s now easyto see there are 3 loops (they form “ V -shapes”), so the answer is 10 · 2 · 3 = 60.
    2 2 2 2