A(n)个数码,恰好分成k个数,k个数积最大

王守恩

8个数码=1,2,3,4,5,6,7,8, 恰好分成2个数, 2个数的积最大是多少？
9个数码=1,2,3,4,5,6,7,8,9, 恰好分成2个数, 2个数的积最大是多少？
9个数码=1,2,3,4,5,6,7,8,9, 恰好分成3个数, 3个数的积最大是多少？
12个数码=1,2,3,4,5,6,7,8,9,0,1,2, 恰好分成2个数, 2个数的积最大是多少？
12个数码=1,2,3,4,5,6,7,8,9,0,1,2, 恰好分成3个数, 3个数的积最大是多少？
12个数码=1,2,3,4,5,6,7,8,9,0,1,2, 恰好分成4个数, 4个数的积最大是多少？
12个数码=1,2,3,4,5,6,7,8,9,0,1,2, 恰好分成5个数, 5个数的积最大是多少？
A(24)={1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,2,3,4},
A(24)个数码, 恰好分成2个数, 2个数的积最大是多少？
A(24)个数码, 恰好分成3个数, 3个数的积最大是多少？
A(24)个数码, 恰好分成4个数, 4个数的积最大是多少？
A(24)个数码, 恰好分成5个数, 5个数的积最大是多少？
A(24)个数码, 恰好分成6个数, 6个数的积最大是多少？
A(24)个数码, 恰好分成7个数, 7个数的积最大是多少？
......
A(n)个数码, 恰好分成k个数, k个数的积最大是多少？
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,......},

northwolves

这个手工推算即可，大数字放在高位，小数字放在低位：

8个数码=1,2,3,4,5,6,7,8, 恰好分成2个数, 2个数的积最大是多少？
9个数码=1,2,3,4,5,6,7,8,9, 恰好分成2个数, 2个数的积最大是多少？
9个数码=1,2,3,4,5,6,7,8,9, 恰好分成3个数, 3个数的积最大是多少？
------------------------------------------
{{8531, 7642}, 65193902}
{{87531, 9642}, 843973902}
{{941, 852, 763}, 611721516}

northwolves

A(24)={1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,2,3,4},
A(24)个数码, 恰好分成2个数, 2个数的积最大是多少？
---------------------------------------------------
{{987654432110, 987654332210}, 975461178599848831263100}

王守恩

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,......},

A(2026)个数码, 恰好分成100个数, 100个数的积最大是多少？——这个想明白了——前面的就简单了。

王守恩

998887766554433221100*4       
998877766554433221100*2       
998877666554433221100*3       
998877665554433221100*3       
998877665544433221100*3       
998877665544333221100*3       
998877665544332221100*3       
998877665544332211100*3       
998877665544332211000*2       
99987766554433221100*2       
99887766554433221100*72       

补充内容 (2025-8-6 16:15):
这个答案有问题,因为思路搞复杂了。

王守恩

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,......},

A(12345)个数码, 恰好分成100个数, 100个数的积最大是多少？——会了, 就不理他。

补充内容 (2025-8-6 16:15):
这个可以有答案！

王守恩

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,  最小数=R(6)。
R(7)=8865421, ——A(49)个数码, 恰好分成7个7位数, 当7个数的积最大时,  最小数=R(7)。
R(8)=88754321,—— A(64)个数码, 恰好分成8个8位数, 当8个数的积最大时,  最小数=R(8)。
R(9)=887654321, ——A(81)个数码, 恰好分成9个9位数, 当9个数的积最大时,  最小数=R(9)。
R(10)=9876543210, ——
R(11)=98765543210,
R(12)=
R(13)=
R(14)=
1——1
1-v
4——2
41
32-v
9——3
941
852
763-v
16——4
9420
8531
7531
6642-v
25——5
95320
95420
86421
86431
77531-v
36——6
964320
965310
965320
875421-v
875431
876421
49——7
9764320
9764320
9765320
9765310
9854311
8865421-v
8875421
64——8
97654320
97654310
97654210
97653210
98643210
98643210
88754321-v
88754321
81——9
976543210
976543210
986543210
987543210
987643210
987653210
987654210
987654310
887654321-v
100——10
9876543210
9876543210
9876543210
9876543210
9876543210
9876543210
9876543210
9876543210
9876543210-v
9876543210
121——11
99776432100
98776443210
98776443210
98766443210
98765543210
98765543210-v
98765543210
98765533210
98765532210
98865432110
98865432110

往前手工还是走不了！各位大侠！可有方法？谢谢！

王守恩

补充一下思路。譬如
64——8——基本盘
9, 9, 9, 9, 9, 9, 8, 8,
8, 8, 8, 8, 7, 7, 7, 7,
7, 7, 6, 6, 6, 6, 6, 6,
5, 5, 5, 5, 5, 5, 4, 4,
4, 4, 4, 4, 4, 3, 3, 3,
3, 3, 3, 3, 2, 2, 2, 2,
2, 2, 2, 1, 1, 1, 1, 1,
1, 1, 0, 0, 0, 0, 0, 0,
64——8——(1)——把第1行搬过来。
9, 9, 9, 9, 9, 9, 8, 8,
64——8——(1a)——按从小到大排列。
8, 8, 9, 9, 9, 9, 9, 9,
64——8——(2)——把第2行搬过来。
8, 8, 9, 9, 9, 9, 9, 9,
8, 8, 8, 8, 7, 7, 7, 7,
64——8——(2a)——按从小到大排列。
8, 8, 9, 9, 9, 9, 9, 9,
8, 8, 7, 7, 7, 7, 8, 8,
64——8——(3)——把第3行搬过来。
8, 8, 9, 9, 9, 9, 9, 9,
8, 8, 7, 7, 7, 7, 8, 8,
7, 7, 6, 6, 6, 6, 6, 6,
64——8——(3a)——按从小到大排列。
8, 8, 9, 9, 9, 9, 9, 9,
8, 8, 7, 7, 7, 7, 8, 8,
7, 7, 6, 6, 6, 6, 6, 6,
64——8——(4)——把第4行搬过来。
8, 8, 9, 9, 9, 9, 9, 9,
8, 8, 7, 7, 7, 7, 8, 8,
7, 7, 6, 6, 6, 6, 6, 6,
5, 5, 5, 5, 5, 5, 4, 4,
64——8——(4a)——按从小到大排列。
8, 8, 9, 9, 9, 9, 9, 9,
8, 8, 7, 7, 7, 7, 8, 8,
7, 7, 6, 6, 6, 6, 6, 6,
5, 5, 5, 5, 5, 5, 4, 4,
64——8——(5)——把第5行搬过来。
8, 8, 9, 9, 9, 9, 9, 9,
8, 8, 7, 7, 7, 7, 8, 8,
7, 7, 6, 6, 6, 6, 6, 6,
5, 5, 5, 5, 5, 5, 4, 4,
4, 4, 4, 4, 4, 3, 3, 3,
64——8——(5a)——按从小到大排列。
8, 8, 9, 9, 9, 9, 9, 9,
8, 8, 7, 7, 7, 7, 8, 8,
7, 7, 6, 6, 6, 6, 6, 6,
5, 5, 5, 5, 5, 5, 4, 4,
4, 4, 3, 4, 4, 4, 3, 3,
64——8——(6)——把第6行搬过来。
8, 8, 9, 9, 9, 9, 9, 9,
8, 8, 7, 7, 7, 7, 8, 8,
7, 7, 6, 6, 6, 6, 6, 6,
5, 5, 5, 5, 5, 5, 4, 4,
4, 4, 3, 4, 4, 4, 3, 3,
3, 3, 3, 3, 2, 2, 2, 2,
64——8——(6a)——按从小到大排列。
8, 8, 9, 9, 9, 9, 9, 9,
8, 8, 7, 7, 7, 7, 8, 8,
7, 7, 6, 6, 6, 6, 6, 6,
5, 5, 5, 5, 5, 5, 4, 4,
4, 4, 3, 4, 4, 4, 3, 3,
3, 3, 3, 3, 2, 2, 2, 2,
64——8——(7)——把第7行搬过来。
8, 8, 9, 9, 9, 9, 9, 9,
8, 8, 7, 7, 7, 7, 8, 8,
7, 7, 6, 6, 6, 6, 6, 6,
5, 5, 5, 5, 5, 5, 4, 4,
4, 4, 3, 4, 4, 4, 3, 3,
3, 3, 3, 3, 2, 2, 2, 2,
2, 2, 2, 1, 1, 1, 1, 1,
64——8——(7a)——按从小到大排列。
8, 8, 9, 9, 9, 9, 9, 9,
8, 8, 7, 7, 7, 7, 8, 8,
7, 7, 6, 6, 6, 6, 6, 6,
5, 5, 5, 5, 5, 5, 4, 4,
4, 4, 3, 4, 4, 4, 3, 3,
3, 3, 3, 3, 2, 2, 2, 2,
2, 2, 2, 1, 1, 1, 1, 1,
64——8——(8)——把第8行搬过来。
8, 8, 9, 9, 9, 9, 9, 9,
8, 8, 7, 7, 7, 7, 8, 8,
7, 7, 6, 6, 6, 6, 6, 6,
5, 5, 5, 5, 5, 5, 4, 4,
4, 4, 3, 4, 4, 4, 3, 3,
3, 3, 3, 3, 2, 2, 2, 2,
2, 2, 2, 1, 1, 1, 1, 1,
1, 1, 0, 0, 0, 0, 0, 0,
至此,这8列表示的8个数,就是题目要找的8个数——若光是找第1列(最小数)会简单些。

hujunhua

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，要求大数字占高位
差最小，使得两数的位数最接近（等长或者a比 b 长一位），并使得高位数字较接近。除了最高位，同位数字 b的要大于a的。
比如{1,2,3,4,5,6,7,8}, a=8531, b=7642
{1,2,3,4,5,6,7,8,9}, a=87531, b=9642

王守恩

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,  最小数=R(6)。
R(7)=8865421, ——A(49)个数码, 恰好分成7个7位数, 当7个数的积最大时,  最小数=R(7)。
R(8)=88754321,—— A(64)个数码, 恰好分成8个8位数, 当8个数的积最大时,  最小数=R(8)。
R(9)=887654321, ——A(81)个数码, 恰好分成9个9位数, 当9个数的积最大时,  最小数=R(9)。
R(10)=9876543210, ——
R(11)=98765543210,

1——1
1,

4——2
3, 4,
2, 1,

9——3
7, 8, 9,
6, 5, 4,
3, 2, 1,

16——4
6, 7, 8, 9,
6, 5, 5, 4,
4, 3, 3, 2,
2, 1, 1, 0,

25——5
7, 8, 8, 9, 9,
7, 6, 6, 5, 5,
5, 4, 4, 3, 4,
3, 2, 3, 2, 2,
1, 1, 1, 0, 0,

36——6
8, 8, 8, 9, 9, 9,
7, 7, 7, 6, 6, 6,
5, 5, 6, 4, 5, 5,
4, 4, 4, 3, 3, 3,
2, 3, 2, 2, 1, 2,
1, 1, 1, 0, 0, 0,

49——7
8, 8, 9, 9, 9, 9, 9,
8, 8, 7, 7, 7, 7, 8,
6, 7, 6, 6, 6, 6, 5,
5, 5, 4, 4, 5, 5, 4,
4, 4, 3, 3, 3, 3, 3,
2, 2, 2, 2, 2, 1, 1,
1, 1, 1, 0, 0, 0, 0,

64——8
8, 8, 9, 9, 9, 9, 9, 9,
8, 8, 7, 7, 7, 7, 8, 8,
7, 7, 6, 6, 6, 6, 6, 6,
5, 5, 5, 5, 5, 5, 4, 4,
4, 4, 3, 4, 4, 4, 3, 3,
3, 3, 3, 3, 2, 2, 2, 2,
2, 2, 2, 1, 1, 1, 1, 1,
1, 1, 0, 0, 0, 0, 0, 0,

81——9
8, 9, 9, 9, 9, 9, 9, 9, 9,
8, 7, 7, 8, 8, 8, 8, 8, 8,
7, 7, 7, 6, 6, 6, 7, 7, 7,
6, 6, 6, 5, 6, 6, 5, 5, 5,
5, 5, 5, 5, 4, 4, 4, 4, 4,
4, 4, 4, 3, 3, 3, 3, 3, 3,
3, 3, 2, 2, 2, 2, 2, 2, 2,
2, 1, 1, 1, 1, 1, 1, 1, 1,
1, 0, 0, 0, 0, 0, 0, 0, 0,

100——10
9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

121——11
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9,
7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 7,
6, 6, 6, 6, 6, 7, 7, 7, 6, 6, 6,
5, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 3, 3, 4, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 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, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

144——12
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 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, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 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, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

169——13
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9,
7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 7,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5,
5, 5, 4, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 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, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

196——14
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9,
8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6,
5, 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, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 1, 2, 2, 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,

225——15
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9,
8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
6, 6, 7, 7, 7, 7, 7, 7, 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, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 2, 3, 3, 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,
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,

8楼的方法没错！！！手工错误难免。往前手工还是走不了！各位大侠！可有方法？谢谢！