Sprouts By Tamsen Hunter Special Topics 2003

Background on Sprouts Invented in 1967 by John H. Conway, and Michael S. Paterson Paterson and Conway were Princeton Professors working at the University of Cambridge Conway once wrote, “The day after sprouts sprouted, it seemed that everyone was playing it.”

Rules for Sprouts 1. Play with a pen and a piece of paper 2. Starting positions are the dots 3. Draw a loop/line (make sure not to cross any other loop/line) 4. Add a dot to the new loop/line (no dot can have more than three lines attached to it.) 5. The game is finished when you will have to cross a loop/line to add a new loop/line

Sprouts Played with 3 dots Step 3 Step 4 Step 5 Step 1 Step 2 Step 6 First Player Second Player First Player Second Player

Step 7Step 8 Sprouts Played with 3 dots First Player wins because there is no move for Player Two. Second Player

Sprouts Played with 1 dot Step 1 Step 2 Step 3 First Player Second Player wins because there is no move for Player One.

Sprouts Every game that starts with n dots; –has a maximum of 3n-1 moves Proof –Each move uses 2 of the openings; one at the end and one at the beginning of the curve –At the same time it adds another dot and therefore adds one more opening –Each time a player goes it decreases the number of openings by one, and a move requires filling two openings –So the game ends when there is only one opening left

Sprouts This means that if a game starts with 4 dots then it must end in at most 11 moves. This means that; –Player One will always win games involving 3, 4 or 5 dots –Player Two will always win games involving 1, 2, or 6 dots

Sprouts Try a game with a partner using more than 6 dots and see who wins. Sprouts is a game for all ages!!