我算了一下前 30 × 30 的 Sprague-Grundy 函数表，如下：

      0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 
   -----------------------------------------------------------------------------------------------
 0 |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 
 1 |  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 
 2 |  0  2  1  0  2  1  3  3  4  4  5  5  6  6  7  7  8  8  9  9 10 10 11 11 12 12 13 13 14 14 15 
 3 |  0  3  0  1  0  1  2  1  2  3  2  3  4  4  4  5  5  5  6  6  6  7  7  7  8  8  8  9  9  9 10 
 4 |  0  4  2  0  1  0  0  1  2  1  1  2  3  2  3  3  4  3  4  4  5  5  5  5  6  6  6  6  7  7  7 
 5 |  0  5  1  1  0  1  0  0  0  1  2  1  2  2  2  3  2  3  3  3  4  3  4  4  4  5  4  5  5  5  6 
 6 |  0  6  3  2  0  0  1  0  0  0  1  1  2  1  1  1  2  2  3  2  2  3  3  3  4  3  4  4  4  4  5 
 7 |  0  7  3  1  1  0  0  1  0  0  0  0  1  1  2  1  1  2  2  2  2  3  2  2  3  3  3  3  4  3  4 
 8 |  0  8  4  2  2  0  0  0  1  0  0  0  0  1  1  1  2  1  1  1  1  2  2  2  3  2  2  3  3  3  3 
 9 |  0  9  4  3  1  1  0  0  0  1  0  0  0  0  0  1  1  1  2  1  1  1  2  2  2  2  2  3  2  2  2 
10 |  0 10  5  2  1  2  1  0  0  0  1  0  0  0  0  0  0  1  1  1  2  1  1  1  2  1  2  2  2  2  3 
11 |  0 11  5  3  2  1  1  0  0  0  0  1  0  0  0  0  0  0  1  1  1  1  2  1  1  1  1  2  2  2  2 
12 |  0 12  6  4  3  2  2  1  0  0  0  0  1  0  0  0  0  0  0  0  1  1  1  1  2  1  1  1  1  1  1 
13 |  0 13  6  4  2  2  1  1  1  0  0  0  0  1  0  0  0  0  0  0  0  0  1  1  1  1  2  1  1  1  1 
14 |  0 14  7  4  3  2  1  2  1  0  0  0  0  0  1  0  0  0  0  0  0  0  0  1  1  1  1  1  2  1  1 
15 |  0 15  7  5  3  3  1  1  1  1  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  1  1  1  1  1  2 
16 |  0 16  8  5  4  2  2  1  2  1  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  1  1  1  1  1 
17 |  0 17  8  5  3  3  2  2  1  1  1  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  1  1  1 
18 |  0 18  9  6  4  3  3  2  1  2  1  1  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  1 
19 |  0 19  9  6  4  3  2  2  1  1  1  1  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0 
20 |  0 20 10  6  5  4  2  2  1  1  2  1  1  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0 
21 |  0 21 10  7  5  3  3  3  2  1  1  1  1  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0 
22 |  0 22 11  7  5  4  3  2  2  2  1  2  1  1  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0 
23 |  0 23 11  7  5  4  3  2  2  2  1  1  1  1  1  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0 
24 |  0 24 12  8  6  4  4  3  3  2  2  1  2  1  1  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0 
25 |  0 25 12  8  6  5  3  3  2  2  1  1  1  1  1  1  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0 
26 |  0 26 13  8  6  4  4  3  2  2  2  1  1  2  1  1  1  0  0  0  0  0  0  0  0  0  1  0  0  0  0 
27 |  0 27 13  9  6  5  4  3  3  3  2  2  1  1  1  1  1  0  0  0  0  0  0  0  0  0  0  1  0  0  0 
28 |  0 28 14  9  7  5  4  4  3  2  2  2  1  1  2  1  1  1  0  0  0  0  0  0  0  0  0  0  1  0  0 
29 |  0 29 14  9  7  5  4  3  3  2  2  2  1  1  1  1  1  1  0  0  0  0  0  0  0  0  0  0  0  1  0 
30 |  0 30 15 10  7  6  5  4  3  2  3  2  1  1  1  2  1  1  1  0  0  0  0  0  0  0  0  0  0  0  1 

发现 “0” 的边缘处的斜率很接近 1.618，于是试着提交了一下，果然 AC 了！
为什么会出现黄金比例系数呢，世界真奇妙。

• 原来是威佐夫的变形啊，谢谢大牛的表了！！ (3487) lijunle 2010-09-15 16:31:36
• Re:发现这题和 1067 一样，也是黄金比例系数。 (191) linulysses 2011-04-23 10:11:03
  • Re:发现这题和 1067 一样，也是黄金比例系数。 (36) ludi 2011-06-04 22:14:58
• 感谢大牛的表 (16) kalao0o 2017-07-03 16:13:02