Number Solitaire

A couple of weeks ago, Laina showed me a solitaire game that she had been playing a lot lately. You begin by drawing a six-by-six square of boxes on a sheet of paper. Lined paper works well because it gives you guidelines. You then put the number one in any square and then continue numerically until you run out of boxes. The catch is that you have to follow a pattern for entering the numbers:

If you're moving up, down, left, or right, you must skip two boxes to enter the next number. If you're moving diagonally, you must skip one box. You can see in the picture that I skipped two boxes to enter "2", then one box diagonally to enter "3", and so on. The goal of the game is to get as high a number as possible. The highest number you could get would be 36, because there are thirty six boxes. My highest ever was 35, and I thought that 36 was impossible. Until today.

In what might be the most boring class ever, I hit the holy grail of 6x6 number solitaire¹. I made it all the way to 36. I thought at first that I would post the solution, but then I decided that I should have other people try. If you get 36, let me know. It took me a couple of weeks. It's a great way to zone out in boring classes.

A friend of mine wrote down every move I made, whether it was a 4 block move (up, down, left, right) or a 3 block move (diagonal) and there was no real pattern, except that 4, 4, 3 happened a bunch of times. Perhaps there is a pattern, but I think if I figured it out the game would lose it's time-wasting appeal.

Maybe I'll try a 7x7 square from now on. Would more squares make it more difficult?

1. I'm not sure if this game has an official name. I did some searching on Google for the name but I kept finding mathematical stuff. [↩]