Signals and Noises

Boat Game

I think of Boat Game as a digital water fountain—it produces a pleasant trickle of sound, is lovely to look at, and makes no demands on the viewer's constant attention or powers of perception.

Boat Game is a math puzzle brought to my attention by a high school student seeking help with its solution. You have a canoe with an odd number of seats (2N+1) arranged in a single file along the length of the canoe. You start with N girls at one end of the canoe, N boys at the other end, leaving the lone empty seat in the middle. The goal is to move the boys to the girls' side and the girls to the boys' side, one at a time, in as few moves as possible. There are only two legal moves, which are similar to those allowed in the game of checkers: 1) any passenger sitting next to the empty seat may move to that seat, and 2) any passenger may jump over an adjacent passenger if there is an empty seat on the other side of that passenger to jump into.

In Boat Game, the puzzle is solved continuously, over and over again, by an algorithm that has been optimized to always find the best solution. Each new iteration of the puzzle starts with a random value of N between 1 and 10 (2 to 20 passengers). Each move in the solution to the puzzle is mapped to a pair of musical notes, the first representing the seat just vacated, the second the newly occupied seat. Thus we essentially hear a mathematical process unfold. For added richness, two identical "solution engines" are running simultaneously, except that one uses a piano sound and the other an organ sound.

Boat Game is intended to be displayed on a computer monitor that is mounted vertically rather than horizontally, so that the moving bars representing the notes appear dripping down the screen rather than across it. The algorithm runs continuously, never repeating. This video captures several minutes' of typical behavior: