Underdog
Underdog is a puzzle about dividing a population into towns so that the underdogs win. Dogs and cats live together on a grid of residents, and the board must be split into towns. In each town the animal with more residents wins it, and the dogs must win more towns than the cats. Simple splits are often easy to win, but the rules make the board harder: no town may be half the size of another town or smaller, so a town of ten residents cannot sit beside a town of five or fewer.
The idea is planning under constraints. Grouping all the cats together can look tempting, but a single large cat town forces the other towns to be small, which breaks the fairness rule. Players must balance the sizes of towns with the animals inside them, placing a few cats among the dogs so that a dog town still wins while the cat towns stay small enough to be legal. The solution is found by trying a split, checking the size rule, counting the towns each animal wins, and then adjusting.
In the Campaign Boss pack on OpenPuzzle.org, every resident starts as a cat. Children place the dogs themselves, as few as they can, then split the board so that the dogs win, and challenge a classmate to win with fewer. With too few dogs no split can win, and that is worth discussing too. Gordon starts with a three-to-two election, so the class can see the rules work before the harder board appears.
- Grades
- 2–6
- Subjects
- Counting & Estimating, Fractions, Shapes & Space
- Kind
- Puzzle
- Original
- Emoji Democracy at MathPickle
Broken TV
Finding Zero
Longest Road