Search: 1^2+5^2+6^2+7^2+8^2+15^2=20^2
a:1 5 6 8
b:1 5 7 7
1*1=+1*1;
A
5*5=+5*5;
AAAAA
AAAAA
AAAAA
AAAAA
AAAAA
6*6=+1*6+5*6;
BBBBBB
BBBBBB
BBBBBB
BBBBBB
BBBBBB
AAAAAA
7*7=+1*7+6*7;
BBBBBBB
BBBBBBB
BBBBBBB
BBBBBBB
BBBBBBB
BBBBBBB
AAAAAAA
8*8=+1*8+7*8;
BBBBBBBB
BBBBBBBB
BBBBBBBB
BBBBBBBB
BBBBBBBB
BBBBBBBB
BBBBBBBB
AAAAAAAA
15*15=+1*5+1*5+1*7+5*7+5*7+5*8+6*7+7*8;
HHHHHHHHGGGGGGG
HHHHHHHHGGGGGGG
HHHHHHHHGGGGGGG
HHHHHHHHGGGGGGG
HHHHHHHHGGGGGGG
HHHHHHHHGGGGGGG
HHHHHHHHCCCCCCC
FFFFFEEEEEDDDDD
FFFFFEEEEEDDDDD
FFFFFEEEEEDDDDD
FFFFFEEEEEDDDDD
FFFFFEEEEEDDDDD
FFFFFEEEEEDDDDD
FFFFFEEEEEDDDDD
FFFFFBBBBBAAAAA
Search: 2^2+3^2+4^2+6^2+10^2+14^2=19^2
a:2 3 4 10
b:2 3 4 10
2*2=+2*2;
AA
AA
3*3=+3*3;
AAA
AAA
AAA
4*4=+2*4+2*4;
BBBB
BBBB
AAAA
AAAA
6*6=+2*3+2*3+3*4+3*4;
DDDDBB
DDDDBB
DDDDBB
CCCCAA
CCCCAA
CCCCAA
10*10=+2*10+2*10+3*10+3*10;
DDDDDDDDDD
DDDDDDDDDD
DDDDDDDDDD
CCCCCCCCCC
CCCCCCCCCC
CCCCCCCCCC
BBBBBBBBBB
BBBBBBBBBB
AAAAAAAAAA
AAAAAAAAAA
14*14=+4*4+4*10+4*10+10*10;
DDDDDDDDDDBBBB
DDDDDDDDDDBBBB
DDDDDDDDDDBBBB
DDDDDDDDDDBBBB
DDDDDDDDDDBBBB
DDDDDDDDDDBBBB
DDDDDDDDDDBBBB
DDDDDDDDDDBBBB
DDDDDDDDDDBBBB
DDDDDDDDDDBBBB
CCCCCCCCCCAAAA
CCCCCCCCCCAAAA
CCCCCCCCCCAAAA
CCCCCCCCCCAAAA
22#附件中最后一个方案$4^2+6^2+8^2+10^2+12^2+13^2=23^2$有两种不同的划分方案，其中一种对称一种不对称。
而对称方案可以排列成非常简单的图案
5刀可以切出5个正方形，而且这个方案好像是唯一的
4个正方形好像4刀不行，当然5刀结果就多了，比如
Search: 2^2+4^2+5^2+6^2=9^2
a:1 1 2 5
b:2 3 4
2*2=+1*2+1*2;
BB
AA
4*4=+1*3+1*3+1*4+2*3;
DDDA
DDDA
BBBA
CCCC
5*5=+2*5+3*5;
BBBBB
BBBBB
BBBBB
AAAAA
AAAAA
6*6=+2*2+1*4+2*4+4*5;
DDDDDB
DDDDDB
DDDDDB
DDDDDB
CCCCAA
CCCCAA
3个正方形可以4刀,比如
Search: 1^2+4^2+8^2=9^2
a:1 4 4
b:1 4 4
1*1=+1*1;
A
4*4=+1*4+1*4+1*4+1*4;
DDDD
CCCC
BBBB
AAAA
8*8=+4*4+4*4+4*4+4*4;
DDDDCCCC
DDDDCCCC
DDDDCCCC
DDDDCCCC
BBBBAAAA
BBBBAAAA
BBBBAAAA
BBBBAAAA
而两个正方形可以3刀:
Search: 3^2+4^2=5^2
a:1 1 3
b:2 3
3*3=+1*3+2*3;
BBB
BBB
AAA
4*4=+1*2+1*2+1*3+3*3;
DDDB
DDDB
DDDA
CCCA
在22#的附件中还发现一个6刀对称的, 贵在大正方形只有17X17。
`2^2+4^2+5^2+6^2+8^2+12^2=17^2`
在22#的附件中发现一个20#的分割的对称拼接
`1^2+4^2+6^2+8^2+10^2+12^2=19^2`
mathe 发表于 2021-9-30 22:36
$1^2+2^2+5^2+6^2+7^2+9^2=14^2$ 有6刀方案:
横向三刀分成1 2 4 7四份
纵向三刀分成1 2 5 6四份
在22#附件中发现的以下组合更有意思，`1^2,2^2,5^2,6^2,7^2`皆为整块，剩下的拼为`9^2`。跟21#相似的特性。
并且`9^2`的组成中也有一块`7^2`, 所以在两块`7^2`中任选一块都可以。
1*1=+1*1;
A
2*2=+2*2;
AA
AA
5*5=+1*5+4*5;
BBBBB
BBBBB
BBBBB
BBBBB
AAAAA
6*6=+2*6+4*6;
BBBBBB
BBBBBB
BBBBBB
BBBBBB
AAAAAA
AAAAAA
7*7=+1*7+6*7;
BBBBBBB
BBBBBBB
BBBBBBB
BBBBBBB
BBBBBBB
BBBBBBB
AAAAAAA
9*9=+1*2+1*2+1*4+1*6+2*4+2*5+2*7+5*7;
HHHHHHHDC
HHHHHHHDC
HHHHHHHDC
HHHHHHHDC
HHHHHHHDA
GGGGGGGDA
GGGGGGGBB
FFFFFEEEE
FFFFFEEEE
7个正方形7刀:
Search: 1^2+2^2+3^2+4^2+5^2+7^2+11^2=15^2
a:1 2 2 5 5
b:1 3 4 7
1*1=+1*1;
A
2*2=+1*2+1*2;
BB
AA
3*3=+1*3+2*3;
BBB
BBB
AAA
4*4=+2*4+2*4;
BBBB
BBBB
AAAA
AAAA
5*5=+1*5+1*5+3*5;
CCCCC
CCCCC
CCCCC
BBBBB
AAAAA
7*7=+2*3+2*7+2*7+3*5;
DDDDDAA
DDDDDAA
DDDDDAA
CCCCCCC
CCCCCCC
BBBBBBB
BBBBBBB
11*11=+1*4+1*7+4*5+4*5+5*7+5*7;
FFFFFFFDDDD
FFFFFFFDDDD
FFFFFFFDDDD
FFFFFFFDDDD
FFFFFFFDDDD
EEEEEEECCCC
EEEEEEECCCC
EEEEEEECCCC
EEEEEEECCCC
EEEEEEECCCC
BBBBBBBAAAA
8个正方形7刀:
Search: 2^2+3^2+5^2+6^2+8^2+9^2+11^2+12^2=22^2
a:2 3 5 6 6
b:2 3 8 9
2*2=+2*2;
AA
AA
3*3=+3*3;
AAA
AAA
AAA
5*5=+2*5+3*5;
BBBBB
BBBBB
BBBBB
AAAAA
AAAAA
6*6=+3*6+3*6;
BBBBBB
BBBBBB
BBBBBB
AAAAAA
AAAAAA
AAAAAA
8*8=+3*8+5*8;
BBBBBBBB
BBBBBBBB
BBBBBBBB
BBBBBBBB
BBBBBBBB
AAAAAAAA
AAAAAAAA
AAAAAAAA
9*9=+3*9+6*9;
BBBBBBBBB
BBBBBBBBB
BBBBBBBBB
BBBBBBBBB
BBBBBBBBB
BBBBBBBBB
AAAAAAAAA
AAAAAAAAA
AAAAAAAAA
11*11=+2*3+2*8+5*9+6*9;
DDDDDDDDDBB
DDDDDDDDDBB
DDDDDDDDDBB
DDDDDDDDDBB
DDDDDDDDDBB
DDDDDDDDDBB
CCCCCCCCCBB
CCCCCCCCCBB
CCCCCCCCCAA
CCCCCCCCCAA
CCCCCCCCCAA
12*12=+2*3+2*6+2*6+2*9+6*8+6*8;
FFFFFFFFDDCC
FFFFFFFFDDCC
FFFFFFFFDDCC
FFFFFFFFDDCC
FFFFFFFFDDCC
FFFFFFFFDDCC
EEEEEEEEDDBB
EEEEEEEEDDBB
EEEEEEEEDDBB
EEEEEEEEAABB
EEEEEEEEAABB
EEEEEEEEAABB
源码: