The math inside

Sprouts

Rules

1
Start: a few dots on the paper
2
Each move joins two dots (a dot may loop back to itself), then a new dot grows on the line
2 used, 1 left Full (3) 3
The new dot already has 2 lines, so 1 use left. A dot allows 3 lines
Cross Through 4
Lines cannot cross, and cannot pass through a dot

Whoever plays the last move wins.

Where it comes from, and questions to think about

A pencil, a sheet of paper, two people. In 1967, John Conway and Michael Paterson at the University of Cambridge invented it. That year is written in a 1991 report from Carnegie Mellon University. The report is called Computer Analysis of Sprouts. Ben Orlin includes the game in Math Games with Bad Drawings. Sprouts on Wikipedia

Questions strong players ask

  • Which dots can still be joined?
  • Can you trap a dot so nothing can reach it?
  • What is different inside a loop and outside it?
Starting dots
First move
Tap to switch. Online, the room host sets this in the room.
Local
Online
Match history