Sprouts

1. Sprouts By Tamsen Hunter Special Topics 2003

2. 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.”

3. 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

4. Step 1 SproutsPlayed with 3 dots Step 3 Step 2 Second Player First Player Step 5 Step 6 Step 4 Second Player First Player First Player

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

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

7. 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

8. 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

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