How to Invent Mathematical Puzzles:
Rush Hour, Sudoku, and Beyond

By Scott Kim, Mar 10, 2011, for the Nueva School. Also presented at the Stanford Math Circle, Mar 9, 2011.
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S U M M A R Y   A N D   R E S O U R C E S

Solving mathematical puzzles is a fun way to improve your problem solving skills. Inventing puzzles takes you even deeper into mathematical thinking, the same way writing a story takes you deeper into language and communicating than reading a story. Here are tips for creating your own Sudoku and Rush Hour puzzles.

HOW TO INVENT A SUDOKU PUZZLE

Twelve Sudoku puzzles
Answers to Sudoku puzzles
Blank grids for creating your own Sudoku Puzzles

1. Start with a blank grid. For ages 7 and under I suggest the 4x4 grid. For ages 8 and above I suggest the 5x5 or 6x6 grid.

2. Fill in numbers to make a complete solution. Then remove numbers, making sure there is just one solution. This is called working backwards. Or try working forwards: fill in numbers until there is a unique solution.

3. Test your puzzle on someone else. Is it solvable? Is it fun?

TAKING IT FURTHER

4. Add a theme by putting your puzzle into a story, or changing the numbers to pictures or letters. Or arrange the numbers to form a picture.

5. Make a sequence of puzzles that go from easy to hard. Like levels in a computer game, a sequence of puzzles lets players get into the game easily, then gradually learn how to solve harder challenges.

6. Change the rules if you want to make something more original. For instance, you can make a larger board, change the region shapes, or change the goal (for instance, require that the diagonals contain all the numbers).

HOW INVENT A RUSH HOUR PUZZLE

Blank grids for creating your own Rush Hour puzzles.
More information about Rush Hour and ThinkFun.

1. Work backwards. Put the escape car at the exit, put other pieces on the board, scramble.

2. Or work forwards. Put pieces on the board one at a time, making sure there is always a solution.