Gerrymandering is the practice of redrawing the boundaries of political districts to favour certain parties or politicians.
On Friday, Texas governor Greg Abbott signed a new redistricting bill with a gerrymandered map that will heavily favour Republicans – and California governor Gavin Newsom plans to retaliate by doing the same in his state for Democrats.
Irresepective of the politics of gerrymandering, however, the ruse conceals some interesting maths. Such as – given a certain distribution of voters, how do you draw a map that makes the minority party win the majority of districts?
It’s exactly this question that underlies today’s puzzles.
In each of the grids below, the challenge is to find the unique electoral map in which the minority colour wins the most regions. A region is defined as a contiguous block of cells that are joined either horizontally or vertically. (A region cannot contain any cells that are only connected diagonally, i.e. via a corner.) Winning a region means having the most cells in that region.
The puzzles were conceived by Brady Forrest, a university student in Toronto, whose online alias is Deckard.
Example
Divide the grid into 3 regions of 3 cells each. Purple, the minority colour, must win the majority of the regions.
To solve using pencil and paper, click here for a print out (and some bonus puzzles). To play on your screen, below each puzzle is a link to an interactive version.
Puzzle 1: Easy
Divide the grid into 5 regions of 5 cells each. Purple, the minority colour, must win the majority of regions.
For an interactive version of this puzzle click here
Puzzle 2: Medium
Divide the grid into 5 regions of 10 cells each. Purple, the minority colour, must win the majority of regions. No ties allowed in any region.
For an interactive version of this puzzle click here
Puzzle 3: Hard
Divide the grid into 7 regions of 7 cells each. Blue, the minority colour, must win the majority of regions. No ties allowed for first place in any region.
For an interactive version of this puzzle click here
I’ll be back at 5pm UK with the solutions.
NO SPOILERS Please discuss the maths of gerrymandering.
Thanks to Deckard for sharing his puzzles. Thanks to Starwort for the interactive versions.
I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
In other Gerry-related news, here’s a fact from my new book, Football School Facts. Gerry Taggart (ex-Bolton) is one of only four Premier League players to have been sent off on their birthdays. The wrong sort of card! This curio and hundreds of others appear in the book, the latest in the long-running series I write with Ben Lyttleton for children aged 7 to 107. Football School Facts is full-colour, hardback, would make an excellent gift, and is available at the Guardian Bookshop.