MathDB

Let

n{}

be a natural number. The playing field for a "Master Sudoku" is composed of the

n(n+1)/2

cells located on or below the main diagonal of an

n\times n

square. A teacher secretly selects

n{}

cells of the playing field and tells his student
[*]the number of selected cells on each row, and [*]that there is one selected cell on each column. The teacher's selected cells form a Master Sudoku if his student can determine them with the given information. How many Master Sudokus are there?
Proposed by T. Amdeberkhan, M. Ruby and F. Petrov

Problem Statement