Earlier today I set three gerrymandering logic puzzles. Here they are again with solutions.
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.
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.
The puzzles were conceived by Brady Forrest (aka Deckard). He talks about the maths behind the puzzle (and shows how to solve them) in this YouTube clip:
All solutions at the bottom.
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
Solutions
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.