[If you want to dive straight into Algebraic Linesweeper, here’s a printable PDF with rules.]
A friend of mine, Jak Marshall, created a pen-and-paper puzzle game called Linesweeper. Here are the rules:
- Draw a single, closed, continuous loop in the empty cells of the grid which never crosses itself or branches.
- The number clue in a cell indicates how many of the 8 adjacent cells are part of the loop (as in the classic computer game Minesweeper); for instance, a ‘0’ means that none of the adjacent cells are part of the loop.
- The loop may not enter a cell with a number.
- The loop may run horizontally or vertically (not diagonally) between centres of adjacent cells (that is, parallel to the grid lines).
- The loop does not need to pass through all the unoccupied cells.
- Each puzzle should have a unique solution.
I think it’s fun and relaxing, and more satisfying to progress and finally connect the loop than fill in the final cells of a Sudoko puzzle. You can also design puzzles that use a bit of simple graph theory: if there is an area that your line visits with only three possible routes in and out, it can only use an even number (two) of these (the loop is in some sense a Eulerian circuit).
- Each letter corresponds to a unique number between 0 and 8.
- Within a puzzle, different letters must correspond to different numbers.
- Each puzzle should still have a unique solution!