When I was a child, I used to play a simple game with pen and paper.
The goal is to fill a 10x10 grid with the numbers from 1 to 100. To start the game, you have to write 1 in a cell, then each turn you can move from the preceding number by jumping 2 cells horizontally or vertically, or by jumping 1 cell diagonally. The difficulty appears when too many cells are occupied, because when you can't move anymore the game is over.
It does not seem too hard, but, believe me, it's almost impossible to solve.
Want to try?
I recently made a web version of this game, and I named it Up to 100.
As many of the things I create, it's open-source, and the code is hosted on GitHub.