1, 5, 2, 10, 3を円環状に並べたものについて
連続に隣り合っているいるものの和を考える
例
1=1
2=2
3=3
4=3+1
5=5
6=1+5
7=5+2
8=1+5+2
9=3+1+5
10=10
11=3+1+5+2
実は1から5*(5-1)+1までのすべての数を作ることが出来る

数字の個数が5以外の場合について、計算機を使って算出した

n=2
[1, 2]
n=3
[1, 2, 4]
[1, 4, 2]
n=4
[1, 2, 6, 4]
[1, 3, 2, 7]
[1, 7, 2, 3]
[1, 4, 6, 2]
n=5
[1, 5, 2, 10, 3]
[1, 3, 10, 2, 5]
n=6
[1, 2, 5, 4, 6, 13]
[1, 2, 7, 4, 12, 5]
[1, 3, 2, 7, 8, 10]
[1, 3, 6, 2, 5, 14]
[1, 7, 3, 2, 4, 14]
[1, 14, 4, 2, 3, 7]
[1, 14, 5, 2, 6, 3]
[1, 10, 8, 7, 2, 3]
[1, 5, 12, 4, 7, 2]
[1, 13, 6, 4, 5, 2]
n=7
n=8
[1, 2, 10, 19, 4, 7, 9, 5]
[1, 8, 2, 3, 21, 4, 12, 6]
[1, 12, 2, 6, 3, 7, 22, 4]
[1, 4, 2, 10, 18, 3, 11, 8]
[1, 3, 8, 2, 16, 7, 15, 5]
[1, 3, 5, 11, 2, 12, 17, 6]
[1, 6, 17, 12, 2, 11, 5, 3]
[1, 5, 15, 7, 16, 2, 8, 3]
[1, 8, 11, 3, 18, 10, 2, 4]
[1, 4, 22, 7, 3, 6, 2, 12]
[1, 6, 12, 4, 21, 3, 2, 8]
[1, 5, 9, 7, 4, 19, 10, 2]
n=9
[1, 2, 4, 8, 16, 5, 18, 9, 10]
[1, 16, 22, 2, 3, 4, 6, 8, 11]
[1, 8, 12, 2, 3, 13, 24, 4, 6]
[1, 14, 8, 2, 28, 3, 6, 7, 4]
[1, 4, 7, 6, 3, 28, 2, 8, 14]
[1, 6, 4, 24, 13, 3, 2, 12, 8]
[1, 11, 8, 6, 4, 3, 2, 22, 16]
[1, 10, 9, 18, 5, 16, 8, 4, 2]
n=10
[1, 2, 6, 18, 22, 7, 5, 16, 4, 10]
[1, 36, 2, 12, 7, 8, 3, 13, 4, 5]
[1, 4, 2, 20, 8, 9, 23, 10, 3, 11]
[1, 18, 3, 2, 8, 4, 29, 11, 9, 6]
[1, 4, 3, 10, 2, 9, 14, 16, 6, 26]
[1, 18, 28, 5, 2, 8, 6, 11, 9, 3]
[1, 3, 9, 11, 6, 8, 2, 5, 28, 18]
[1, 26, 6, 16, 14, 9, 2, 10, 3, 4]
[1, 6, 9, 11, 29, 4, 8, 2, 3, 18]
[1, 11, 3, 10, 23, 9, 8, 20, 2, 4]
[1, 5, 4, 13, 3, 8, 7, 12, 2, 36]
[1, 10, 4, 16, 5, 7, 22, 18, 6, 2]
n=11
n=12
[1, 2, 14, 4, 37, 7, 8, 27, 5, 6, 13, 9]
[1, 2, 9, 8, 14, 4, 43, 7, 6, 10, 5, 24]
[1, 2, 12, 31, 25, 4, 9, 10, 7, 11, 16, 5]
[1, 2, 14, 12, 32, 19, 6, 5, 4, 18, 13, 7]
[1, 7, 2, 22, 4, 16, 3, 11, 29, 21, 12, 5]
[1, 11, 2, 8, 7, 25, 6, 3, 27, 20, 19, 4]
[1, 6, 2, 33, 17, 14, 12, 10, 15, 3, 16, 4]
[1, 14, 3, 2, 4, 7, 21, 8, 25, 10, 12, 26]
[1, 31, 10, 2, 4, 3, 8, 13, 5, 20, 14, 22]
[1, 9, 48, 2, 4, 18, 5, 11, 3, 12, 13, 7]
[1, 8, 5, 2, 18, 11, 10, 22, 6, 24, 23, 3]
[1, 6, 28, 2, 13, 16, 23, 19, 5, 9, 8, 3]
[1, 3, 12, 34, 21, 2, 8, 9, 5, 6, 7, 25]
[1, 4, 7, 3, 16, 2, 6, 17, 20, 9, 13, 35]
[1, 35, 26, 3, 11, 2, 4, 21, 7, 5, 10, 8]
[1, 15, 5, 3, 25, 2, 7, 4, 6, 12, 14, 39]
[1, 41, 8, 4, 17, 2, 3, 6, 7, 20, 10, 14]
[1, 7, 6, 16, 15, 2, 9, 10, 40, 3, 20, 4]
[1, 4, 20, 3, 40, 10, 9, 2, 15, 16, 6, 7]
[1, 14, 10, 20, 7, 6, 3, 2, 17, 4, 8, 41]
[1, 39, 14, 12, 6, 4, 7, 2, 25, 3, 5, 15]
[1, 8, 10, 5, 7, 21, 4, 2, 11, 3, 26, 35]
[1, 35, 13, 9, 20, 17, 6, 2, 16, 3, 7, 4]
[1, 25, 7, 6, 5, 9, 8, 2, 21, 34, 12, 3]
[1, 3, 8, 9, 5, 19, 23, 16, 13, 2, 28, 6]
[1, 3, 23, 24, 6, 22, 10, 11, 18, 2, 5, 8]
[1, 7, 13, 12, 3, 11, 5, 18, 4, 2, 48, 9]
[1, 22, 14, 20, 5, 13, 8, 3, 4, 2, 10, 31]
[1, 26, 12, 10, 25, 8, 21, 7, 4, 2, 3, 14]
[1, 4, 16, 3, 15, 10, 12, 14, 17, 33, 2, 6]
[1, 4, 19, 20, 27, 3, 6, 25, 7, 8, 2, 11]
[1, 5, 12, 21, 29, 11, 3, 16, 4, 22, 2, 7]
[1, 7, 13, 18, 4, 5, 6, 19, 32, 12, 14, 2]
[1, 5, 16, 11, 7, 10, 9, 4, 25, 31, 12, 2]
[1, 24, 5, 10, 6, 7, 43, 4, 14, 8, 9, 2]
[1, 9, 13, 6, 5, 27, 8, 7, 37, 4, 14, 2]