Tower of Hanoi

Materials needed

Playing board: 2 pieces of colored paper, taped together horizontally (draw three squares across them with an X in one square)

Tower: 5 foamboard squares, cut one each 2x2, 3x3, 4x4, 5x5, 6x6 inches

Score sheet: table with two columns for number of pieces in tower stack and number of moves

Rules

Teams of two play -- one moves while the other team member counts the number of moves and records the best score

Only one piece can be moved at a time; it must be a top piece. It may be moved to ANY open square or onto a larger piece. A larger piece can never be placed on top of a smaller piece. Pieces may be moved backwards into an open square or onto a larger piece.

The goal is to reassemble the tower at the opposite end of the playing board in the least amount of moves. Begin by placing a tower of one piece and moving it to the other end -- this level takes one move. Next stack two pieces on the X on the playing board. Figure out how to move this tower to the opposite end in the least amount of moves. Record your moves on the score sheet. Continue adding a piece and playing the new level.

For older students, have them find the pattern in the number of moves as you add pieces to the tower. For capable students (high school or above), have them generate a formula that predicts the number of moves for a tower of N pieces.

History

The legend says that monks in a temple are moving 64 gold disks from one room to another. There is a resting place between the rooms. When the monks finish their task, the universe disappear.