论坛 › 难题征解 › A(n)个数码,恰好分成k个数,k个数积最大

王守恩 发表于 2025-8-6 16:12:31

前面的有问题吗？来个反例就行。谢谢！

天马行空往前走一走！

256——16——基本解。
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
7, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 7, 7, 7, 7,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 4, 4, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 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,

256——16——"0"是可以去掉的。
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
7, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 7, 7, 7, 7,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 4, 4, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1,

256——16——相同数码的"行"是可以去掉的。
8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9,
7, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 7, 7, 7, 7,
6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5,
4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 4, 4, 3, 3, 3, 3,
2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1,

256——16——相同数码的"列"也是可以去掉的。
8, 8, 8, 9, 9, 9, 9,
7, 7, 8, 7, 7, 7, 7,
7, 7, 7, 6, 6, 7, 7,
6, 6, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 4, 5,
4, 4, 4, 3, 4, 3, 3,
2, 3, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 1,
1, 1, 1,

256——16——每个数 - 1。
7, 7, 7, 8, 8, 8, 8,
6, 6, 7, 6, 6, 6, 6,
6, 6, 6, 5, 5, 6, 6,
5, 5, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 3, 4,
3, 3, 3, 2, 3, 2, 2,
1, 2, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 0,
0, 0, 0,
256——16——去掉"0"。
7, 7, 7, 8, 8, 8, 8,
6, 6, 7, 6, 6, 6, 6,
6, 6, 6, 5, 5, 6, 6,
5, 5, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 3, 4,
3, 3, 3, 2, 3, 2, 2,
1, 2, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1,

256——16——每个数 - 1。
6, 6, 6, 7, 7, 7, 7,
5, 5, 6, 5, 5, 5, 5,
5, 5, 5, 4, 4, 5, 5,
4, 4, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 2, 3,
2, 2, 2, 1, 2, 1, 1,
0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,

256——16——去掉末尾"0"——结论没变。
6, 6, 6, 7, 7, 7, 7,
5, 5, 6, 5, 5, 5, 5,
5, 5, 5, 4, 4, 5, 5,
4, 4, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 2, 3,
2, 2, 2, 1, 2, 1, 1,
0, 1,   

王守恩 发表于 2025-8-7 08:16:57

hujunhua 发表于 2025-8-6 09:48
2ab=(a+b)^2-(a-b)^2
所以分成子集拼成两个数时，保持和最大，差最小，则乘积最大。
和最大，要求大数字占 ...
A = {1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,......},

R(1)=1,——A(1)个数码, 恰好分成1个1位数, 当1个数的积最大时,最小1位数=R(1)。
R(2)=32, ——A(4)个数码, 恰好分成2个2位数, 当2个数的积最大时,最小2位数=R(2)。
R(3)=763, ——A(9)个数码, 恰好分成3个3位数, 当3个数的积最大时,最小3位数=R(3)。
R(4)=6642, ——A(16)个数码, 恰好分成4个4位数, 当4个数的积最大时,最小4位数=R(4)。
R(5)=77531, ——A(25)个数码, 恰好分成5个5位数, 当5个数的积最大时,最小5位数=R(5)。
R(6)=875421, ——A(36)个数码, 恰好分成6个6位数, 当6个数的积最大时,最小6位数=R(6)。
R(7)=8865421,
R(8)=88754321,
R(9)=887654321,
R(10)=9876543210,
R(11)=98765543210,
R(12)=987765433210,
R(13)=9877665433210,
R(14)=98876554432210,
R(15)=988766554332110,
R(16)=9887766544322110,
R(17)=98887665544322110,
R(18)=988877655443322110,
R(19)=
R(20)=

尊敬的 hujunhua！您是我的引路人(很多帖子我还在经常回看)。OEIS没有这串数,麻烦您去申报(这串数是您的)。谢谢！

补充内容 (2025-8-10 10:01):
R(12)错啦！R(12)=987765432210,——其它都是对的——R(19),R(20)手工计算太难了。

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