Question

迷因玄師

從1到9選出四個不重複的數字，組成一個四位數，且必須是3的倍數，共有多少種排法？

Select [Permutations
选择 [排列
[Range [1, 9], {4}], Mod [FromDigits [#], 3] ==
[范围
[模余[根据数字构建数
{1, 2, 3,6}, {1, 2, 3, 9}, {1, 2, 4, 5}, {1, 2, 4, 8},
{1, 2, 5, 4}, {1, 2, 5, 7}, {1, 2, 6, 3}, {1, 2, 6, 9},
{1, 4, 7, 6}, {1, 4, 7, 9},
{1, 5, 2, 4},
{1, 5, 2, 7},
{1, 4, 8, 2},
{1, 5, 3, 6},
{1, 5, 6,
9},
{1, 5, 4, 8},
{1, 5, 6, 3},
{1, 5, 8, 4},
{1, 5, 8, 7}, {1, 5, 9, 3},
{1, 2, 7, 5}, {1, 2,7,8}, {1, 2, 8, 4}, {1, 2, 8, 7}, {1, 2, 9, 3},
{1, 2,9,6}, {1, 3, 2, 6}, {1, 3, 2, 9}, {1, 3, 4, 7}, {1, 3, 5, 6},
{1, 3, 5, 9}, {1, 3,6, 2}, {1, 3, 6, 5}, {1, 3, 6, 8}, {1, 3, 7, 4},
{1, 3, 8,6}, {1, 3, 8, 9}, {1, 3,9, 2}, {1, 3, 9, 5}, {1, 3, 9, 8},
{1, 4, 2, 5}, {1, 4, 2, 8}, {1, 4, 3, 7}, {1, 4, 5, 2}, {1, 4, 5, 8},
{1, 4, 6, 7}, {1, 4, 7, 3},
{1, 4, 8, 5}, {1, 4, 9, 7},
{1, 5, 3, 9}, {1, 5, 4, 2},
{1, 5,7, 2}, {1, 5, 7, 8},
{1, 5,9,6}, {1, 6, 2,3}, {1, 6, 2, 9}, {1, 6, 3, 2}, {1, 6, 3, 5},
{1, 6, 3,8}, {1, 6, 4, 7}, {1, 6, 5, 3}, {1, 6, 5, 9}, {1, 6, 7, 4},
{1, 6, 8,3}, {1, 6, 8, 9}, {1, 6, 9, 2}, {1, 6, 9, 5}, {1, 6, 9,8},
{1, 7, 2, 5}, {1, 7, 2, 8}, {1, 7, 3, 4}, {1, 7, 4, 3}, {1, 7, 4, 6},
{1, 7, 4, 9}, {1, 7, 5, 2}, {1, 7, 5,8}, {1, 7, 6, 4}, {1, 7, 8, 2),
{1,7,8, 5}, {1, 7, 9, 4}, {1, 8, 2, 4}, {1, 8, 2, 7}, {1, 8, 3, 6},
{1, 8, 3,9}, {1, 8, 4,2}, {1, 8, 4, 5}, {1, 8, 5, 4}, {1, 8, 5, 7},
{1,8,6,3}, {1, 8,6,9}, {1, 8,7,2}, {1, 8,7, 5}, {1,8,9,3)
(1,8,9,6}, {1, 9, 2,3}, {1, 9, 2,6}, {1, 9, 3, 2), (1,9, 3, 5),
(1,9,3,8}, {1,9,4,7}, {1,9,5,3}, {1, 9,5,6), (1,9,6,2),
(1,9,6,5}, {1,9,6,8}, (1,9,7,4), (1,9,8,3), (1,9.8.6),
(2, 1, 3, 6), (2, 1, 3, 9), (2, 1, 4, 5), (2, 1, 4, 8), (2, 1, 5, 4)
12 15 71 (2 1 6 31 12 1 691 (71
(7

(9, 7, 5, 6), (9, 7, 6, 2), (9, 7, 6, 5), (9, 7,
{9, 7, 8,6}, {9, 8, 1, 3}, {9, 8, 1, 6}, {9, 8,
{9, 8, 3, 4}, {9, 8, 3, 7}, {9, 8, 4, 3}, {9, 8,
{9, 8, 6, 1}, {9, 8, 6, 4}, {9, 8, 6,7}, {9, 8,
n[-]:=length[Select
# ], 3 ] == 0 & ]]
Length(Select [Permutations[Range[1, 9], {4}],
长度
[选择 [排列
|范围
Mod [FromDigits[1], 3] == 0 & ] ]
[模余[根据数字构建数
[ Permutations [ Range [1, 9], {4}], M
Dut[50)= 1008
X

Answer 1

qn

將數字分類：
a. 被3整除：3,6,9
b. 除以3餘1：1,4,7
c. 除以3餘2：2,5,8
先考慮組合：
aabc: C³₂C³₁C³₁=27
abbb: C³₁C³₃=3
accc: C³₁C³₃=3
bbcc: C³₂C³₂=9
共27+3+3+9=42種
每種組合都有4!=24種排列
所以全部有42×24=1008種排法