It is a puzzle that is played with three stakes and a variable number of discs.
In the exhibition version, the stakes are arranged in triangles instead of in rows (classic version) and you can play with up to 8 discs.
How to play
The rules are simple:
1) You must move the whole tower from one stake to another, one disk at a time;
2) A large disk cannot cover a smaller disk.
This puzzle is immediately understandable, solves quickly with just a few disks (the advice is to start with 3 disks), but it gets quite complicated as the number of disks increases: the number of moves needed to solve it increases very quickly. The minimum number of moves, errors excluded, is perfectly predictable: if n is the number of disks you play with, you will need at least 2^n-1 moves to solve it.
With 1 disc, 2^1-1=2-1=1 move will be needed.
With 2 discs, 2^2-1=4-1=3 moves will be needed.
With 3 discs, 2^3-1=8-1=7 moves will be needed.
And so on…
Put another way, every time you add a floor, you need twice as many moves plus one. This second relationship is more obvious than the first as you play: each time you add a disk (below the others) you will first have to repeat the same operations as in the previous round to clear it, then move the added disk, then repeat the moves in reverse to cover it.
Teaching links: Exponentials – Hidden in the solution of the game are the well-known powers of 2, recalling among other things the binary notation of numbers (in fact, there is an interpretation of the game in this key, see link below).
Teaching links: Mathematical successions – To prove (by induction) that the minimum number of moves to solve the game with n planes is 2^n-1 we use a result from succession theory:
Teaching links: Programming – The triangle arrangement of the Hanoi tower also highlights the algorithm of moves that can be found as a solution (in a nutshell: even-numbered discs always move in one direction, odd-numbered discs move in the opposite direction). Following this procedure, a computer can solve the problem without knowing the rules of the game, while a human could move the tower correctly while thinking about the shopping list, whistling.
How to build
- Horizontal pallet 120×120 cm
- Vertical pallet 100 x 215 cm
- Wood and cardboard triangle base 100 cm side, with n. 3 wood rods (properly secured)
- n. max 8 different color discs (MDF) / 2-4 cm thickness
- Cardboard title panel
- Cardboard panel with explanation and photo (100×100 cm)
- Cardboard panel with explanation (65×10 cm) – appropriately xed (velcro? double-sided tape?)