Ladder Logic

Ladder Logic gives you three pegs and a stack of discs sitting on the left one, largest at the bottom. Move the whole stack to the right peg. You may move only the top disc of a peg, one at a time, and you may never place a larger disc on top of a smaller one.

The interesting part is the count. Three discs can be done in 7 moves, four in 15, five in 31 — each extra disc a little more than doubles the work, because moving a stack of five means moving a stack of four out of the way first, then the big disc, then the stack of four back. That is 2 to the power of the number of discs, minus 1, and the game shows your move count against that minimum so a student can see the doubling happen rather than be told about it.

It rewards planning over poking. Students who move at random will get there eventually on three discs and stall on five; students who spot the repeating pattern — move the smaller tower, move the big one, move the smaller tower back — solve any size. It is a good introduction to recursion and to exponential growth for anyone in upper primary and above.