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 3×3 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 4×4 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 3×3 grid the answer is 2 lines

For the 4×4 grid the answer is 3 lines

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

Oliver Slay
(@oliverslay)

Something like this? pic.twitter.com/ZWs7stBAFK


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.





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