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.

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.*