PATTERNS OF HANOI
by Matt Farr

SUBJECT:
Algebra/Geometry

TOPIC:
Discovery of Patterns


Matt Farr
To obtain a downloadable copy of the worksheet that accompanies this bulletin board, click on the button below.

TITLE: Patterns of Hanoi

SUBJECT: Algebra/Geometry

TOPIC: Discovery of patterns

INTERACTIVITY: The interactivity is the student having to complete the puzzle in order to complete the worksheet. They must complete the puzzle three times, once each for 3, 4, and 5 discs.

DIRECTIONS FOR USE: Complete the following table while playing the Tower of Hanoi. You will input how many times each disk moves, the smallest total number of moves, and the move sequence. Perform the operations for 3, 4, and 5 discs. The rules are following:

  1. Remove all piles from the pegs except for the one you are currently using.
  2. Object - Move the pile of discs from one peg to another.
  3. You may only move one disc at a time.
  4. No disc may be on top of a smaller disc.

TIME: 15-25 minutes depending on how long it takes the student to catch on to the puzzle.

SPECIAL CONSTRUCTION: A shelf made out of foam board with 3 wooden pegs screwed into the top. Also, three sets of discs, ones of 3, 4, and 5, made out of foam board.

CREDIT: This is worth 5 bonus points. There are 4 possible points for completing the table correctly and then the final point is for the last question in which they will solve the puzzle based on the legend.

OTHER COMMENTS: You need to have one set of discs on one peg and then have the other two pegs clear in order to complete the puzzle.

Matt Farr
Spring 2006