每个信封装两封信,要求每个信封与两封信有不同的编号, 有多少种装法?

王守恩 · 发表于 2025-1-5 17:34:21

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每个信封装信A,信B两封信, 信封,信A,信B都有编号1～N, 要求每个信封与信有不同的编号, 有多少种装法?

每个信封装信A,信B两封信, 信封,信A,信B都有编号1～N, 要求每个信封与信=3个不同的编号, 有多少种装法?

aimisiyou · 发表于 2025-1-6 08:57:20

应该是这个数列。

王守恩 · 发表于 2025-1-6 10:07:44

每个信封装信A,信B两封信,  信封,信A,信B都有编号1～N,  要求每个信封与信有不同的编号,  有多少种装法?
N=2。有1种装法。
22,11=信封。
11,22,
N=3。有4种装法。
33,22,11=信封。
11,33,22=十位数有1,2,3,  个位数有1,2,3。
12,31,23,
21,13,32,
22,11,33,
N=4。有81种装法。
44,33,22,11=信封。
11,22,33,44,
11,22,34,43,
11,22,43,34,
11,22,44,33,
11,24,33,42,
11,24,43,32,
11,42,33,24,
11,42,34,23,
11,44,33,22,

每个信封装信A,信B两封信,  信封,信A,信B都有编号1～N,  要求每个信封与信=3个不同的编号,  有多少种装法?
N=2。有0种装法。
22,11=信封。
11,22=x
N=3。有2种装法。
33,22,11=信封。
11,33,22=x
12,31,23,
12,33,21=x
21,13,32,
N=4。有24种装法。
44,33,22,11=信封。
12,21,34,43,
12,21,43,34,
12,24,31,43,
12,41,34,23,

aimisiyou · 发表于 2025-1-6 10:56:41

本帖最后由 aimisiyou 于 2025-1-6 10:58 编辑

王守恩发表于 2025-1-6 10:07
每个信封装信A,信B两封信, 信封,信A,信B都有编号1～N, 要求每个信封与信有不同的编号, 有多少种装法?
N= ...

三个不同编号：F（1）=F（2）=0，F（3）=2，F（4）=24，,F（5）=552，F（6）=21280……

王守恩 · 发表于 2025-1-6 12:43:25

先大致捋一捋。欢迎批评。

每个信封装信A一封信,  信封,信A都有编号1～N,  要求每个信封与信有不同的编号,  有多少种装法?
{0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570, 176214841, 2290792932, 32071101049, 481066515734}
Table[(Round[n!/E]), {n, 15}]

每个信封装信A,信B两封信,  信封,信A,信B都有编号1～N,  要求每个信封与信有不同的编号,  有多少种装法?
{0, 1, 4, 81, 1936, 70225, 3437316, 220017889, 17821182016, 1782120871521, 215636596084900, 31051670188655281, 5247732257301156624, 1028555522495168900401, 231424992560450869558756,}
Table[(Round[n!/E])^2, {n, 15}]

每个信封装信A,信B两封信,  信封,信A,信B都有编号1～N,  要求每个信封与信=3个不同的编号,  有多少种装法?
{0, 0, 2, 24, 552, 21280, 1073760, 70299264, 5792853248, 587159944704,

每个信封装信A,信B,信c三封信,  信封,信A,信B都有编号1～N,  要求每个信封与信有不同的编号,  有多少种装法?
{0, 1, 8, 729, 85184, 18609625, 6372783864, 3263525347537, 2379056514407936, 2379061860766545681, 3166530689770439993000, 5471765125078330345225321, 12021467964053894989684181568, 32986908096449554419082687620649,}
Table[(Round[n!/E])^3, {n, 14}]

每个信封装信A,信B,信c三封信,  信封,信A,信B,信c都有编号1～N,  要求每个信封与信=4个不同的编号,  有多少种装法?

aimisiyou · 发表于 2025-1-6 18:00:57

王守恩发表于 2025-1-6 12:43
先大致捋一捋。欢迎批评。

每个信封装信A一封信, 信封,信A都有编号1～N, 要求每个信封与信有不同的编号, ...

0,0,0,24,1344,393120……

王守恩 · 发表于 2025-1-8 07:50:00

本帖最后由王守恩于 2025-1-8 08:01 编辑

aimisiyou 发表于 2025-1-6 10:56
三个不同编号：F（1）=F（2）=0，F（3）=2，F（4）=24，,F（5）=552，F（6）=21280…… ...

请教 aimisiyou！N=5。有552种装法=12*46, 46?我这里怎么数也数不了46种。谢谢aimisiyou ！
每个信封装信A,信B两封信, 信封,信A,信B都有编号1～N, 要求每个信封与信=3个不同的编号, 有多少种装法?
N=2。有0种装法。
22,11=信封。
11,22=x
N=3。有2种装法。
33,22,11=信封。
11,33,22=x
12,31,23,
12,33,21=x
21,13,32,
N=4。有24种装法。
44,33,22,11=信封。
12,21,34,43,
12,21,43,34,
12,24,31,43,
12,41,34,23,
......4*6=24种装法没问题。
N=5。有552种装法=12*46,12=2*6=2*(12,13,14,23,24,34), 46?我这里怎么数也数不了46种。
55,44,33,22,11=信封。
12,21,45,34,53=01
12,21,45,53,34=02
12,21,54,35,43=03
12,21,54,43,35=04
12,23,41,35,54=05
12,23,41,54,35=06
12,23,45,31,54=07
12,23,45,51,34=08
12,25,41,34,53=09
12,25,41,53,34=10
12,25,51,34,43=11
12,25,51,43,34=12
12,25,54,31,43=13
12,31,24,45,53=14
12,31,24,53,45=15
12,31,25,43,54=16
12,31,25,54,43=17
12,31,45,53,24=18
12,31,45,54,23=19
12,31,54,43,25=20
12,31,54,45,23=21
12,35,21,43,54=22
12,35,21,54,43=23
12,35,24,41,53=24
12,35,24,51,43=25
12,35,51,43,24=26
12,35,54,41,23=27
12,51,24,35,43=28
12,51,24,43,35=29
12,51,25,34,43=30
12,51,25,43,34=31
12,51,45,34,23=32
12,53,21,34,45=33
12,53,21,45,34=34
12,52,24,31,45=35
12,53,24,41,35=36
12,53,25,41,34=37
12,53,41,34,25=38
12,53,41,35,24=39
12,53,45,31,24=40

aimisiyou · 发表于 2025-1-8 08:50:15

王守恩发表于 2025-1-8 07:50
请教 aimisiyou！N=5。有552种装法=12*46, 46?我这里怎么数也数不了46种。谢谢aimisiyou ！
每个信封装信A ...

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((2 5) (1 4) (4 1) (5 3) (3 2)) ((2 5) (1 4) (4 2) (5 3) (3 1)) ((2 3) (1 4) (5 1) (3 5) (4 2)) ((2 3) (1 4) (5 2) (3 5) (4 1)) ((2 3) (1 5) (5 4) (3 1) (4 2)) ((2 3) (1 5) (5 4) (3 2) (4 1)) ((2 4) (1 3) (5 1) (3 5) (4 2)) ((2 4) (1 3) (5 2) (3 5) (4 1)) ((2 4) (1 5) (5 1) (3 2) (4 3)) ((2 4) (1 5) (5 2) (3 1) (4 3))
((2 5) (1 3) (5 4) (3 1) (4 2)) ((2 5) (1 3) (5 4) (3 2) (4 1)) ((2 5) (1 4) (5 1) (3 2) (4 3)) ((2 5) (1 4) (5 2) (3 1) (4 3)) ((2 3) (3 4) (1 5) (5 1) (4 2)) ((2 3) (3 4) (1 5) (5 2) (4 1)) ((2 3) (3 5) (1 4) (5 1) (4 2)) ((2 3) (3 5) (1 4) (5 2) (4 1)) ((2 4) (3 1) (1 5) (5 2) (4 3)) ((2 4) (3 1) (1 5) (5 3) (4 2))
((2 4) (3 5) (1 2) (5 1) (4 3)) ((2 4) (3 5) (1 2) (5 3) (4 1)) ((2 5) (3 1) (1 4) (5 2) (4 3)) ((2 5) (3 1) (1 4) (5 3) (4 2)) ((2 5) (3 4) (1 2) (5 1) (4 3)) ((2 5) (3 4) (1 2) (5 3) (4 1)) ((2 3) (3 1) (4 5) (5 2) (1 4)) ((2 3) (3 4) (4 5) (5 1) (1 2)) ((2 3) (3 5) (4 1) (5 2) (1 4)) ((2 3) (3 5) (4 2) (5 1) (1 4))
((2 4) (3 1) (4 5) (5 2) (1 3)) ((2 4) (3 1) (4 5) (5 3) (1 2)) ((2 4) (3 5) (4 1) (5 2) (1 3)) ((2 4) (3 5) (4 1) (5 3) (1 2)) ((2 4) (3 5) (4 2) (5 1) (1 3)) ((2 5) (3 1) (4 2) (5 3) (1 4)) ((2 5) (3 4) (4 1) (5 2) (1 3)) ((2 5) (3 4) (4 1) (5 3) (1 2)) ((2 5) (3 4) (4 2) (5 1) (1 3)) ((2 3) (3 1) (5 4) (1 5) (4 2))
((2 3) (3 4) (5 1) (1 5) (4 2)) ((2 3) (3 4) (5 2) (1 5) (4 1)) ((2 3) (3 5) (5 4) (1 2) (4 1)) ((2 4) (3 1) (5 2) (1 5) (4 3)) ((2 4) (3 5) (5 1) (1 2) (4 3)) ((2 4) (3 5) (5 1) (1 3) (4 2)) ((2 4) (3 5) (5 2) (1 3) (4 1)) ((2 5) (3 1) (5 4) (1 2) (4 3)) ((2 5) (3 1) (5 4) (1 3) (4 2)) ((2 5) (3 4) (5 1) (1 2) (4 3))
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((2 5) (4 1) (1 2) (5 3) (3 4)) ((2 5) (4 1) (1 4) (5 3) (3 2)) ((2 5) (4 3) (1 2) (5 1) (3 4)) ((2 5) (4 3) (1 4) (5 1) (3 2)) ((2 5) (4 3) (1 4) (5 2) (3 1)) ((2 3) (4 1) (5 2) (1 5) (3 4)) ((2 3) (4 1) (5 4) (1 5) (3 2)) ((2 3) (4 5) (5 1) (1 2) (3 4)) ((2 3) (4 5) (5 4) (1 2) (3 1)) ((2 4) (4 3) (5 1) (1 5) (3 2))
((2 4) (4 3) (5 2) (1 5) (3 1)) ((2 4) (4 5) (5 1) (1 3) (3 2)) ((2 4) (4 5) (5 2) (1 3) (3 1)) ((2 5) (4 1) (5 2) (1 3) (3 4)) ((2 5) (4 1) (5 4) (1 3) (3 2)) ((2 5) (4 3) (5 1) (1 2) (3 4)) ((2 5) (4 3) (5 4) (1 2) (3 1)) ((2 3) (4 1) (5 2) (3 5) (1 4)) ((2 3) (4 1) (5 4) (3 5) (1 2)) ((2 3) (4 5) (5 1) (3 2) (1 4))
((2 3) (4 5) (5 2) (3 1) (1 4)) ((2 3) (4 5) (5 4) (3 1) (1 2)) ((2 4) (4 1) (5 2) (3 5) (1 3)) ((2 4) (4 3) (5 1) (3 5) (1 2)) ((2 4) (4 5) (5 1) (3 2) (1 3)) ((2 4) (4 5) (5 2) (3 1) (1 3)) ((2 5) (4 1) (5 4) (3 2) (1 3)) ((2 5) (4 3) (5 1) (3 2) (1 4)) ((2 5) (4 3) (5 2) (3 1) (1 4)) ((2 5) (4 3) (5 4) (3 1) (1 2))
((2 3) (5 1) (1 4) (3 5) (4 2)) ((2 3) (5 4) (1 2) (3 5) (4 1)) ((2 3) (5 4) (1 5) (3 1) (4 2)) ((2 3) (5 4) (1 5) (3 2) (4 1)) ((2 4) (5 1) (1 2) (3 5) (4 3)) ((2 4) (5 1) (1 5) (3 2) (4 3)) ((2 4) (5 3) (1 2) (3 5) (4 1)) ((2 4) (5 3) (1 5) (3 1) (4 2)) ((2 4) (5 3) (1 5) (3 2) (4 1)) ((2 5) (5 1) (1 4) (3 2) (4 3))
((2 5) (5 3) (1 4) (3 1) (4 2)) ((2 5) (5 3) (1 4) (3 2) (4 1)) ((2 5) (5 4) (1 2) (3 1) (4 3)) ((2 3) (5 1) (4 2) (1 5) (3 4)) ((2 3) (5 1) (4 5) (1 2) (3 4)) ((2 3) (5 4) (4 1) (1 5) (3 2)) ((2 3) (5 4) (4 2) (1 5) (3 1)) ((2 3) (5 4) (4 5) (1 2) (3 1)) ((2 4) (5 1) (4 5) (1 3) (3 2)) ((2 4) (5 3) (4 1) (1 5) (3 2))
((2 4) (5 3) (4 2) (1 5) (3 1)) ((2 4) (5 3) (4 5) (1 2) (3 1)) ((2 5) (5 1) (4 2) (1 3) (3 4)) ((2 5) (5 3) (4 1) (1 2) (3 4)) ((2 5) (5 4) (4 1) (1 3) (3 2)) ((2 5) (5 4) (4 2) (1 3) (3 1)) ((2 3) (5 1) (4 2) (3 5) (1 4)) ((2 3) (5 1) (4 5) (3 2) (1 4)) ((2 3) (5 4) (4 1) (3 5) (1 2)) ((2 3) (5 4) (4 5) (3 1) (1 2))
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((3 5) (1 4) (4 1) (5 2) (2 3)) ((3 5) (1 4) (4 2) (5 1) (2 3)) ((3 5) (1 4) (4 2) (5 3) (2 1)) ((3 2) (1 3) (5 4) (2 5) (4 1)) ((3 2) (1 4) (5 1) (2 5) (4 3)) ((3 2) (1 5) (5 4) (2 1) (4 3)) ((3 2) (1 5) (5 4) (2 3) (4 1)) ((3 4) (1 3) (5 1) (2 5) (4 2)) ((3 4) (1 3) (5 2) (2 5) (4 1)) ((3 4) (1 5) (5 1) (2 3) (4 2))
((3 4) (1 5) (5 2) (2 1) (4 3)) ((3 4) (1 5) (5 2) (2 3) (4 1)) ((3 5) (1 3) (5 4) (2 1) (4 2)) ((3 5) (1 4) (5 1) (2 3) (4 2)) ((3 5) (1 4) (5 2) (2 1) (4 3)) ((3 5) (1 4) (5 2) (2 3) (4 1)) ((3 2) (4 1) (1 5) (5 3) (2 4)) ((3 2) (4 3) (1 5) (5 1) (2 4)) ((3 2) (4 5) (1 4) (5 1) (2 3)) ((3 2) (4 5) (1 4) (5 3) (2 1))
((3 4) (4 1) (1 5) (5 2) (2 3)) ((3 4) (4 3) (1 5) (5 2) (2 1)) ((3 4) (4 5) (1 2) (5 1) (2 3)) ((3 4) (4 5) (1 2) (5 3) (2 1)) ((3 5) (4 1) (1 2) (5 3) (2 4)) ((3 5) (4 1) (1 4) (5 2) (2 3)) ((3 5) (4 3) (1 2) (5 1) (2 4)) ((3 5) (4 3) (1 4) (5 2) (2 1)) ((3 2) (4 1) (2 5) (5 3) (1 4)) ((3 2) (4 3) (2 5) (5 1) (1 4))
((3 2) (4 5) (2 1) (5 3) (1 4)) ((3 2) (4 5) (2 4) (5 1) (1 3)) ((3 4) (4 1) (2 5) (5 2) (1 3)) ((3 4) (4 1) (2 5) (5 3) (1 2)) ((3 4) (4 3) (2 5) (5 1) (1 2)) ((3 4) (4 5) (2 1) (5 2) (1 3)) ((3 4) (4 5) (2 1) (5 3) (1 2)) ((3 5) (4 1) (2 4) (5 2) (1 3)) ((3 5) (4 1) (2 4) (5 3) (1 2)) ((3 5) (4 3) (2 1) (5 2) (1 4))
((3 5) (4 3) (2 4) (5 1) (1 2)) ((3 2) (4 1) (5 4) (1 5) (2 3)) ((3 2) (4 3) (5 1) (1 5) (2 4)) ((3 2) (4 3) (5 4) (1 5) (2 1)) ((3 2) (4 5) (5 1) (1 3) (2 4)) ((3 2) (4 5) (5 4) (1 3) (2 1)) ((3 4) (4 1) (5 2) (1 5) (2 3)) ((3 4) (4 3) (5 2) (1 5) (2 1)) ((3 4) (4 5) (5 1) (1 2) (2 3)) ((3 4) (4 5) (5 2) (1 3) (2 1))
((3 5) (4 1) (5 2) (1 3) (2 4)) ((3 5) (4 1) (5 4) (1 2) (2 3)) ((3 5) (4 3) (5 1) (1 2) (2 4)) ((3 5) (4 3) (5 4) (1 2) (2 1)) ((3 2) (4 1) (5 4) (2 5) (1 3)) ((3 2) (4 3) (5 1) (2 5) (1 4)) ((3 2) (4 5) (5 1) (2 3) (1 4)) ((3 2) (4 5) (5 4) (2 1) (1 3)) ((3 4) (4 1) (5 2) (2 5) (1 3)) ((3 4) (4 3) (5 1) (2 5) (1 2))
((3 4) (4 5) (5 1) (2 3) (1 2)) ((3 4) (4 5) (5 2) (2 1) (1 3)) ((3 5) (4 1) (5 2) (2 3) (1 4)) ((3 5) (4 1) (5 4) (2 3) (1 2)) ((3 5) (4 3) (5 2) (2 1) (1 4)) ((3 5) (4 3) (5 4) (2 1) (1 2)) ((3 2) (5 1) (1 4) (2 5) (4 3)) ((3 2) (5 3) (1 4) (2 5) (4 1)) ((3 2) (5 4) (1 5) (2 1) (4 3)) ((3 2) (5 4) (1 5) (2 3) (4 1))
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王守恩 · 发表于 2025-1-8 09:56:49

aimisiyou 发表于 2025-1-8 08:50
((2 3) (1 4) (4 5) (5 1) (3 2)) ((2 3) (1 4) (4 5) (5 2) (3 1)) ((2 3) (1 5) (4 1) (5 2) (3 4)) (( ...

((1 1) (2 2) (3 3) (4 4) (5 5))=信封
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((2 3) (5 4) (1 5) (3 1) (4 2)) -40
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((2 3) (5 4) (4 5) (3 1) (1 2)) -46

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