# Research in Scientific Computing in Undergraduate Education

### Sprouts

Sprouts is a two-person game invented by mathematicians John Horton Conway and Michael S. Paterson at Cambridge University in 1967.

The game begins with a number of spots:

Players take turns drawing a line -straight or curved – between existing spots, and adding a new spot in the middle of the new line:

The rules are:

• Lines must not touch or cross any line except at a designated spot.
• No spot may have more than three lines attached to it. A line from a spot to itself counts as two attached lines and new spots are counted as having two lines already attached to them.
• The player who makes the last move wins.

The problem, for a given number of spots is to determine when the first player has a winning strategy, and when the second player has a winning strategy.

It is conjectured that that the first player has a winning strategy when the number of spots is congruent to 3, 4, or 5, modulo 6.

The complexity of analysis grows very rapidly with the initial number of spots.

The misère form of the game is when the last player to move loses.