Tower Trade is a paper adaptation to the traditionally wooden Towers of Hanoi puzzle. In the classic version, a wooden base supports three equally spaced dowels, usually aligned in a row, although the earliest version of this puzzle is reputed to have had the dowels arranged in an equilateral triangle. Six – this number varies — circular disks of differing diameters are stacked on one of the three posts. The disks are arranged by size with the largest diameter one on the bottom and the smallest one on top. The challenge in the puzzle is to transfer all six disks to another post while following two rules:
- only one disk may be moved at a time and
- a larger diameter disk may never be placed on top of a smaller diameter one.
While this is a difficult task, most people can do it if they are persistent. The real challenges when working with the Towers of Hanoi are learning its patterns and finding a way to transfer all the disks in the minimum number of moves.
The best way to work with the Towers of Hanoi is to have a wooden version of this puzzle for every student. My wife did this by having her father, a retired educator who enjoys woodworking, build 33 of the puzzles for her class. He made them quite inexpensively out of particle board. Richard Thiessen, AIMS President and our resident woodworking expert, makes his towers out of medium density fiberboard (MDF). MDF, which is used to make cabinets, is readily available and is only slightly more expensive than particle board. MDF has a couple of great advantages over particle board – it saws cleanly and it doesn’t leave the rough edges the particle board does. To make the construction process much faster and easier, both Richard and my father-in-law cut square, rather than circular, disks. If your local high school has a woodshop, it might be worth seeing if you can get a class set of the puzzles made for you. (See * at the end of this post for the dimensions to Richard Thiessen’s version of the Towers of Hanoi.)
Since many of you do not have access to a woodshop, I am indebted to Richard Thiessen for the viable idea of a paper version which is presented here. Each student needs a set of six different-sized rectangles which represent the six disks viewed from the side. The second sheet (base) contains four sets of “disks” which can be copied on construction paper or tagboard and then cut out.
This puzzle can be modified for different grade levels simply by changing the number of disks. With six disks, it takes a minimum of 63 moves to transfer the tower to another post. This might be fine for older students, but too frustrating for younger ones. Four disks (15 moves) or five disks (31 moves) might be more appropriate for younger students. As mentioned earlier, every student needs to have a Towers of Hanoi puzzle. Provide lots of time for students to work with this puzzle and challenge them to transfer the disks in the fewest moves possible.
Download and copy this sheet on construction paper or tagboard. Each student will need to cut apart one set of rectangles for the Tower Trade puzzle.
Using your rectangles, build a tower on the left post as in diagram below. The largest rectangle must be on the bottom and the others stacked on top of it, ordered by size with the smallest on top.
The challenge in this puzzle is to transfer all the rectangles to a different post while following these rules:
- Move only one rectangle at a time.
- A larger rectangle can never be placed on top of a smaller one.
*Base – 12 inches by 3 3/4 inches by 3 3/4 inches.
Disk – Six, ranging from 1-inch square to 3 1/2-inch square, all 1/2 inch thick.
Posts – three 3/8-inch dowels 4 inches long in holes drilled at, 2, 6, 10 inches along the center line of the base.