Cutting apart a chessboard

Not that any of us would do such a thing, but if we did, and wanted to cut it to 64 separate squares, how many cuts would it take? A single cut goes between any two rows or columns to the other end, cutting the board or part thereof in two. For example the first cut could be between the columns e and f, making two rectangles, A1-E8 and F1-H8. The second would cut one of the pieces in two, so you might end up with, say, A1-E8, F1-H6 and F7-H8. That procedure would be continued until all 64 squares are separate.

I get the same answer for each attempt I have tried.

Reveal Hidden Content

It makes sense, since no cut can cross another cut.

Perfect sense indeed, as each cut, regardless of whether it splits off one square or many, increases the number of pieces by one. 🙂

And if the cuts didn't have to be straight (but still followed the edges of the squares) then the number would be considerably less.

I don't think so.

You can still increase the total number of pieces by only one.

Agreed. If a "cut" ends when a piece of the board is falls into two pieces, n - 1 is how many it takes where n is the number of pieces. Of course, if a cut is defined differently, a whole new problem is found. If a cut is a line that follows goes between the squares, ending at an intersection from which there are no routes out.. it could be doable with as few as Reveal Hidden Content?

Agreed it comes down to the definition of a cut. When I made my earlier statement I didn't define the separation of the board into 2 pieces as a complete cut - I envisaged cutting from one edge of the original board to another edge following a diagonal / stepped path but not turning back on a previous direction. Visualise cutting steps into the board starting at one corner. I also came up with 14.

Interesting 14 is also the answer if the straight cuts can cross previous cuts (without rearranging)

Not a coincidence. Every intersection on the board has four lines leading into it, so no cut can end there if none starts there. That leaves 7 end points on each side of the board, 4 x 7 = 28; each cut removes 2 of them; 28 : 2 = 14.