## Posts

Showing posts from September, 2018

### Brute-forcing a seemingly simple number puzzle

Something was bothering me for almost two decades. It was a pen and paper game that I learned when I was around 13. The rules are simple: on an empty 10x10 grid (100 squares in total) you put a number 1 on an arbitrary square. Starting from that square you can move horizontally or vertically jumping over two squares or diagonally jumping over one square. There you can place number 2. Your task is to reach number 100, filling all squares. You can not visit already visited squares. Here is an example of a solved game with a reduced 5x5 grid, starting at top-left corner:

12414225162158201310182311471536172212919 On the other hand, if the program makes bad choices, we might get stuck without reaching the perfect score of 25 (on a reduced 5x5 grid):

18291613517141047153619121811 Notice how we got stuck at number 19, unable to move anywhere and fill six remaining gaps. On an original 10x10 grid I never managed to reach the perfect score of 100. Countless hours wasted at school, of trial and …