Tower of London

About the Tower of London exercise

Planning a trip to the shops in an order that saves steps, packing the car so the heavy bags go in first, clearing a shelf to reach the jar at the back: a lot of everyday life asks for a few moves to be thought through before the first one is made. The Tower of London puzzle practices exactly that, with three colored balls and three pegs.

This is a free online Tower of London. The balls sit on pegs that hold three, two and one ball, and a picture shows how they should end up. Move one ball at a time, from the top of a peg, until your board matches the picture, in as few moves as you can. Tap a ball to pick it up and tap a peg to put it on, or drag it. Nothing is timed unless a clinician sets a time.

How the Tower of London works

The puzzle comes from planning research in the early 1980s, where it was built as a simpler cousin of the Tower of Hanoi. Every puzzle has a fewest number of moves, and the interest is in finding it: the obvious first move is not always on a shortest way.

1. Look at the picture and find where each ball has to end up.
2. Work out which ball has to go in first. The bottom ball of a stack goes in before the balls on top of it.
3. Plan the first few moves in your head, including any ball that has to step out of the way.
4. Move one ball at a time and check the board against the picture as you go.

What Tower of London practices

Thinking ahead

Seeing two or three moves ahead before touching a ball is the heart of the puzzle. Longer puzzles ask for more of the plan to be held in mind at once.

Holding back the quick move

Some puzzles have a move that looks right, a ball straight onto its place, that is not on a shortest way. Spotting it and waiting is part of the practice.

Working within limits

Each peg holds only so many balls, so a plan has to fit the space. Sometimes a ball has to be parked out of the way first.

Checking against a picture

The goal picture stays on screen the whole time, so the board can be compared with it after every move.

How the tool works and what it records

Three free presets: balls with puzzles of 2 to 3 moves, balls with 4 to 5 moves, and three discs (the Tower of Hanoi), with 6, 6 and 4 puzzles a round. Each puzzle is chosen by a search through every position of the board, 36 of them with three balls, and a round goes from fewer moves to more, each puzzle starting where the last one ended. The first round of the day opens with a one-move try-out that is not counted. Pro unlocks the dials: 3, 4 or 5 balls, pegs that are short, middle and tall or all the same height, puzzles of 2 to 3, 4 to 5, 6 to 7, or 8 or more moves, 4 to 12 puzzles a round, and a time for each puzzle of 1, 2 or 3 minutes, which is off by default. Always free: showing the fewest moves, shapes on the balls, large print and high contrast.

A picked-up ball lifts above the pegs with a ring, and dashed circles show where it has room to land. A move the rules do not allow is not made: the ball stays in the hand and the reason is written out. At the end of a round the results show the puzzles finished, the puzzles finished in the fewest moves, the moves made against the fewest possible, the typical time before the first move and per puzzle, and tries at a full peg. Each puzzle opens to your moves beside a shortest way, and either can be played again. Signed-in users get 5 free rounds per tool per day, and once a day a free account can play a round with every dial; Pro removes the cap, adds a PDF round record and saves rounds to a session log.

The disc puzzle: the Tower of Hanoi

The Tower of Hanoi is the older puzzle, from 1883: discs of different sizes on three pegs, where a bigger disc never goes on a smaller one. Moving a whole tower of three discs takes 7 moves at the fewest, four discs 15 and five discs 31.

Here it runs on the same board with the same two taps. The free preset starts from part-built towers, so the first puzzles are short, 3 to 7 moves with three discs, and each one ends with all the discs in one tower. A move that would put a bigger disc on a smaller one is not made, and the reason is written out. Pro adds four and five discs, and the whole tower to move from one peg to another.

Screen or paper?

There is no printed version of this puzzle. The screen sets up every position, keeps each move within the rules, and keeps count without anyone writing anything down, which suits a short session at a table or a few rounds at home. For planning practice on paper, the executive function guide lists the store's planning and sequencing worksheets.

There is a executive function guide on rehabworksheets.com, with printable practice to try alongside.

Using it well

• Plan first, then move. Before touching a ball, say the first two or three moves out loud. Research on the puzzle found that planning the whole way before moving helps people solve more puzzles.
• Start at 2 to 3 moves. Begin with the first preset, even when it feels easy. Move up a band when most puzzles finish in the fewest moves and the time before the first move is short.
• Keep the fewest moves showing. Knowing how many moves a puzzle needs turns it into a plan to find rather than a hunt. Turn it off later for a different kind of puzzle.
• Start a puzzle again when it helps. Start this puzzle again puts every ball back where the puzzle began. It is counted once, with no fuss, and the picture stays the same.
• Stop while it is pleasant. A few puzzles done calmly are worth more than a long round done tired. End a round at any time; the results show the puzzles so far.

Common questions