# What is the name of this puzzle type? How to create one? nxn grid where you select n cells with different numbers

I want to create a specific puzzle, but I'm wondering if it already has a name, and if I can find some pointers on how to make it hard.

I have a NxN grid filled with numbers going from 1 to N. I want to find the only set of N cells, that:

• Range from 1 to N
• Have one cell per row/column
• Let me see if I understand you right: The solver is given an N*N grid of numbers going from 1 to N, and must select N cells that are all in different rows and different columns, and all contain different numbers? And you want to design such puzzles where there's only one solution?
– xnor
Commented Jul 12 at 9:17
• Yes,exactly ! Thank you ! Commented Jul 12 at 9:26
• So basically sudoku but N doesn’t necessarily equal 9 and there is no 3x3 box constraint? Commented Jul 12 at 16:34
• @EvanSemet No, you start with a filled grid, and to solve it you have to remove numbers until there are only N numbers left - one in each column, one in each row, one of each value. Commented Jul 12 at 21:34

The solution is called a transversal in an $$n \times n$$ array with $$n$$ symbols (for example, in a Latin square): https://en.wikipedia.org/wiki/Latin_square#Transversals_and_rainbow_matchings