2: 8 7 11 6 9 3 14 2 10 4 12 1 13 5 8
3: 8 7 11 5 10 2 14 3 9 4 13 1 12 6 8
4: 8 7 11 1 14 2 10 3 13 4 9 5 12 6 8
5: 8 6 12 5 9 7 10 3 13 2 11 1 14 4 8
6: 8 6 12 5 9 4 13 3 10 2 14 1 11 7 8
7: 8 6 12 4 10 7 9 3 14 1 11 2 13 5 8
8: 8 6 12 3 11 1 14 2 10 7 9 4 13 5 8
9: 8 6 12 1 13 4 9 3 14 2 10 5 11 7 8
10: 8 6 12 1 13 2 11 5 10 7 9 3 14 4 8
11: 8 5 13 4 9 7 10 2 14 1 11 3 12 6 8
12: 8 5 13 2 11 1 14 3 9 7 10 4 12 6 8
13: 8 5 13 1 12 4 10 2 14 3 9 6 11 7 8
14: 8 5 13 1 12 3 11 6 9 7 10 2 14 4 8
15: 8 4 14 3 9 7 10 5 11 2 13 1 12 6 8
16: 8 4 14 2 10 7 9 6 11 3 12 1 13 5 8
17: 8 4 14 2 10 3 13 1 12 5 9 6 11 7 8
18: 8 4 14 1 11 2 13 3 10 7 9 5 12 6 8 本帖最后由 dlpg070 于 2019-5-15 19:24 编辑
northwolves 发表于 2019-5-15 10:41
1: 8 7 11 6 9 5 12 1 13 3 10 2 14 4 8
2: 8 7 11 6 9 3 14...
谢谢northwolves得到全部18组解
我得到的1组解对应这里的第4组解
为了直观欣赏,我画出了全部18幅图,
但为节约资源,只列出第1,第18幅
----------------
本帖最后由 葡萄糖 于 2019-5-16 01:29 编辑
northwolves 发表于 2019-5-15 10:41
1: 8 7 11 6 9 5 12 1 13 3 10 2 14 4 8
2: 8 7 11 6 9 3 14 2 10 4 12 1 13 5 8
3: 8 7 11 5 10 2 14 3 9 4 13 1 12 6 8
4: 8 7 11 1 14 2 10 3 13 4 9 5 12 6 8
5: 8 6 12 5 9 7 10 3 13 2 11 1 14 4 8 ...
值得注意的是，在列出的18个排列中，有等价的（即“从左往右数”与“从右往左数”）
最终可以约简为以下九个：
\begin{align*}
\rlap{\overbrace{\phantom{8+7+11}}^{26}}8+7+
\rlap{\underbrace{\phantom{11+6+9}}_{26}}11+6+
\rlap{\overbrace{\phantom{9+5+12}}^{26}}9+5+
\rlap{\underbrace{\phantom{12+1+13}}_{26}}12+1+
\rlap{\overbrace{\phantom{13+3+10}}^{26}}13+3+
\rlap{\underbrace{\phantom{10+2+14}}_{26}}10+2+
\rlap{\overbrace{\phantom{14+4+8}}^{26}}14+4+8
\\
\rlap{\overbrace{\phantom{8+7+11}}^{26}}8+7+
\rlap{\underbrace{\phantom{11+6+9}}_{26}}11+6+
\rlap{\overbrace{\phantom{9+3+14}}^{26}}9+3+
\rlap{\underbrace{\phantom{14+2+10}}_{26}}14+2+
\rlap{\overbrace{\phantom{10+4+12}}^{26}}10+4+
\rlap{\underbrace{\phantom{12+1+13}}_{26}}12+1+
\rlap{\overbrace{\phantom{13+5+8}}^{26}}13+5+8
\\
\rlap{\overbrace{\phantom{8+7+11}}^{26}}8+7+
\rlap{\underbrace{\phantom{11+5+10}}_{26}}11+5+
\rlap{\overbrace{\phantom{10+2+14}}^{26}}10+2+
\rlap{\underbrace{\phantom{14+3+9}}_{26}}14+3+
\rlap{\overbrace{\phantom{9+4+13}}^{26}}9+4+
\rlap{\underbrace{\phantom{13+1+12}}_{26}}13+1+
\rlap{\overbrace{\phantom{12+6+8}}^{26}}12+6+8
\\
\rlap{\overbrace{\phantom{8+7+11}}^{26}}8+7+
\rlap{\underbrace{\phantom{11+1+14}}_{26}}11+1+
\rlap{\overbrace{\phantom{14+2+10}}^{26}}14+2+
\rlap{\underbrace{\phantom{10+3+13}}_{26}}10+3+
\rlap{\overbrace{\phantom{13+4+9}}^{26}}13+4+
\rlap{\underbrace{\phantom{9+5+12}}_{26}}9+5+
\rlap{\overbrace{\phantom{12+6+8}}^{26}}12+6+8
\\
\rlap{\overbrace{\phantom{8+6+12}}^{26}}8+6+
\rlap{\underbrace{\phantom{12+5+9}}_{26}}12+5+
\rlap{\overbrace{\phantom{9+7+10}}^{26}}9+7+
\rlap{\underbrace{\phantom{10+3+13}}_{26}}10+3+
\rlap{\overbrace{\phantom{13+2+11}}^{26}}13+2+
\rlap{\underbrace{\phantom{11+1+14}}_{26}}11+1+
\rlap{\overbrace{\phantom{14+4+8}}^{26}}14+4+8
\\
\rlap{\overbrace{\phantom{8+6+12}}^{26}}8+6+
\rlap{\underbrace{\phantom{12+4+10}}_{26}}12+4+
\rlap{\overbrace{\phantom{10+7+9}}^{26}}10+7+
\rlap{\underbrace{\phantom{9+3+14}}_{26}}9+3+
\rlap{\overbrace{\phantom{14+1+11}}^{26}}14+1+
\rlap{\underbrace{\phantom{11+2+13}}_{26}}11+2+
\rlap{\overbrace{\phantom{13+5+8}}^{26}}13+5+8
\\
\rlap{\overbrace{\phantom{8+6+12}}^{26}}8+6+
\rlap{\underbrace{\phantom{12+3+11}}_{26}}12+3+
\rlap{\overbrace{\phantom{11+1+14}}^{26}}11+1+
\rlap{\underbrace{\phantom{14+2+10}}_{26}}14+2+
\rlap{\overbrace{\phantom{10+7+9}}^{26}}10+7+
\rlap{\underbrace{\phantom{9+4+13}}_{26}}9+4+
\rlap{\overbrace{\phantom{13+5+8}}^{26}}13+5+8
\\
\rlap{\overbrace{\phantom{8+6+12}}^{26}}8+6+
\rlap{\underbrace{\phantom{12+1+13}}_{26}}12+1+
\rlap{\overbrace{\phantom{13+2+11}}^{26}}13+2+
\rlap{\underbrace{\phantom{11+5+10}}_{26}}11+5+
\rlap{\overbrace{\phantom{10+7+9}}^{26}}10+7+
\rlap{\underbrace{\phantom{9+3+14}}_{26}}9+3+
\rlap{\overbrace{\phantom{14+4+8}}^{26}}14+4+8
\\
\rlap{\overbrace{\phantom{8+5+13}}^{26}}8+5+
\rlap{\underbrace{\phantom{13+1+12}}_{26}}13+1+
\rlap{\overbrace{\phantom{12+3+11}}^{26}}12+3+
\rlap{\underbrace{\phantom{11+6+9}}_{26}}11+6+
\rlap{\overbrace{\phantom{9+7+10}}^{26}}9+7+
\rlap{\underbrace{\phantom{10+2+14}}_{26}}10+2+
\rlap{\overbrace{\phantom{14+4+8}}^{26}}14+4+8
\end{align*}
本帖最后由 dlpg070 于 2019-5-16 18:39 编辑
dlpg070 发表于 2019-5-15 19:19
谢谢northwolves得到全部18组解
我得到的1组解对应这里的第4组解
为了直观欣赏,我画出了全部18幅图,
...
修改图形尺寸,多图排列
18个图形,可以直观看到葡萄糖指出的逆向排列现象
反方向排列对照:
1---17
2---13
3---9
4---6
5---18
7---12
8---11
10---15
14---16
测试效果如下:
------------------ 本帖最后由 chyanog 于 2020-1-2 18:40 编辑
http://www.magic-squares.net/perimeter-2.htm
http://recmath.org/Magic%20Squares/perimeter-2.htm
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