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I find the problem of calculating $n \times n$ Young tableaux from here. I can get the number of $3\times 3$ Young tableaux by violent enumeration is $42$： Partition[#, 3] & /@ Select[Permutations …

Five of the 10 actors can only sing, two can only dance, and three can both sing and dance. Now, how many kinds of selection methods are there to perform a program that requires two people to dance an …

Four couples a are sitting around a round table, in which husband and wife can not be adjacent. How many different seating plans are there? I want to get as many simple calculations as possible. (so …

To plant trees at the center of each small square in a 3 * 4 rectangular area, it is required that there should be no continuous number of three (or more) trees in three directions of Horizontal, vert …

Eight different boys and five different girls are in a row. Girls are required to be next to each other. How many ways are there (the answer is $9!\times5!$)? Cases[Permutations[Array[boy, 8]~Join~Arr …

I want to find the minimum number of swaps required to reset an array. This problem has many applications in linear algebra. The key point of this question is to find the number of closed loops in thi …

x1 , x2 , x3 , x4 and x5 can only be taken from {-1,1,2,4}. How to set a custom number field to solve this equation. NumberField = {-1, 1, 2, 4}; Solve[Mod[x1 + x2 + x3 + x4 + x5, 3] == 0, {x1, x2, …

If there are grammatical or terminological errors in the following description, please help correct: In some problems, it is necessary to find out what minimum number of exchanges can change a list in …

This problem is the fifth question of 1996 Chinese High School Mathematics League or Chinese Mathematical Olympiad in Senior: Choose several colors from the given six different colors to dye six faces …

A054247: Number of n X n binary matrices under action of dihedral group of the square D_4. (*半念浮生*) g[list_] := {list, Reverse /@ list, Reverse@list, Reverse /@ Reverse@list}; g1[list_] := (g[list …

I want to solve this problem: The number 6 can be written as a palindromic sum in exactly eight different ways: (1,1,1,1,1,1),(1,1,2,1,1),(1,2,2,1),(1,4,1),(2,1,1,2),(2,2,2),(3,3),(6) We shall define …

Divide the 14 elements {A, B, C, C, C, C, D, D, D, D, E, E, E, E} into 7 groups (one group all have two elements), and I want to find out how many kinds of methods there are without repetition. (Sort …

This code can only solve the 3 * 3 matrix: list = Permutations[Range[9], {9}]; matrix = Partition[#, 3] & /@ list; answer = Det /@ matrix; m = Max[answer]; pos = Flatten[Position[answer, m]]; matrix[ …