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

Question

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:

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
So basically sudoku but N doesn’t necessarily equal 9 and there is no 3x3 box constraint? — Evan Semet, 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. — Jaap Scherphuis, Commented Jul 12 at 21:34

RobPratt · Accepted Answer · 2024-07-12 17:06:03Z

1

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

answered Jul 12 at 17:06

RobPratt

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$\begingroup$ Thank you! I wasn't specificaly looking for a latin square, I didn't mind if numbers repeated on rows/columns, as long as there was only a single possible transversal. But my question was quite large, so I'll mark the answer as solved, as it greatly helped me. Again, many thanks! $\endgroup$
– Liam Stygian
Commented Jul 16 at 14:36

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