Did you solve it? The Zorro puzzle

Antonio Banderas in The Legend of Zorro, from 2005, Photograph: Allstar/COLUMBIA PICTURES

In my puzzle column earlier today I set you these problems about slicing through a square grid:

1) What is the least number of straight lines you need to draw across a 3x3 square grid so that every cell in the grid has at least one of the lines passing through it.

2) What is the least number of straight lines you need to draw across a 4x4 square grid so that every cell in the grid has at least one of the lines passing through it.

3) What is the least number of lines you need to draw across a n x n square grid so that every cell in the grid has at least one of the lines passing through it.

Solution

For the 3x3 grid the answer is 2 lines

For the 4x4 grid the answer is 3 lines

Thanks to reader for Oliver Slay for colour-coding some example solutions, including for 5x5 and 6x6. His image constitutes a ‘proof without words’ that with any n x n grid we can do it with n – 1 lines.

Something like this? pic.twitter.com/ZWs7stBAFK

— Oliver Slay (@oliverslay) May 20, 2019

Thanks to Carlos D’Andrea of the University of Barcelona for suggesting today’s puzzle.

I’ll be back in two weeks.

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.