Planning

Tower of London test that separates planning from moving

Rearrange three beads on three pegs of different heights to match a target board, in as few moves as the board allows. The clock starts when the board paints and is read twice — at your first move, which is the planning interval, and at your last, which is the moving interval. Two people who solve a five-move problem in five moves can spend those two intervals completely differently.

12 problems
Minimums proved by search
Two intervals per problem

Twelve arrangements to reach, one bead at a time, each with a proved minimum between two and six moves — 53 moves of solution if every one is taken perfectly. The page starts a stopwatch when the board appears and reads it twice: once at your first move and once at your last.

The three rules of the board

The pegs are different heights: the left one holds three beads, the middle one two, the right one exactly one. That asymmetry is the puzzle — with three equal pegs most of these problems would be trivial.
One bead moves at a time, and only the top bead of a peg. Beads are the same size, so nothing here is about which bead may sit on which.
Every problem states the fewest moves that can reach the target, worked out by searching all 36 arrangements the board can take. Beating it is impossible; matching it is the score.

The warm-ups are not timed against anything and tell you afterwards how your move count compared with the minimum. Neither of them reaches the numbers below.

The pause and the moves, read together

The pause before the first move is the only part of a problem where planning can happen, and it is what separates two people with the same move count. A total time cannot tell a long think from a long fumble, and a move count alone cannot see the pause at all, so the result prints both side by side and neither is added to the other:

Pause before moving	Moves	The usual reading
Long	At the minimum	The route was worked out before the hands moved.
Short	At the minimum	The board was easy enough to see whole.
Short	Well above it	The route was found by trying moves on the board.
Long	Well above it	A plan was formed and then lost partway through.

The result also checks whether your pause grew with the size of the problem, which is the signature of planning ahead rather than searching on the board. The task comes from Shallice (1982), Specific impairments of planning, Philosophical Transactions of the Royal Society of London B, built to look for a failure of planning that is neither slowness nor clumsiness — which is exactly what splitting the pause from the moves makes visible.

A board small enough to prove every answer

Three beads on pegs that hold three, two and one can be arranged only 36 ways, and from any of them there are two to four legal moves. That graph is small enough to search completely, so the minimum shown above your board is a shortest path found by breadth-first search, not an estimate — and the same search generates fresh problems at a stated length. The longest shortest path anywhere on this board is eight moves; the twelve problems run from two to six, 53 moves of solution if none is wasted.

The unequal pegs are the whole difficulty. With room everywhere there is always somewhere to park a bead, and most targets fall in one or two obvious moves. The one-bead peg is a bottleneck: whatever goes there has to come off before anything else can use it, and the six-move problems need six moves because the short peg forces a detour. Trying to lift from an empty peg or drop onto a full one is refused and counted apart from your moves — a rule not held in mind is a different failure from a plan that was not good enough. A problem ends on the target, at six moves over the minimum, or when you choose to move on.

Abandoning a rule that has stopped working, rather than planning a route, is the Wisconsin card sorting test; cancelling an action already under way is the stop signal task.

Comparing a run with anything else

Can I compare my result with a clinical Tower of London score?

No, and the obstacle is the problem set rather than the browser. The standardized versions ship a fixed problem set with its own normative data, and the norms only apply to that problem set. A page that generates its own start and goal states has no claim on them. These twelve boards are drawn from a seed, so the page prints raw counts and two intervals rather than a percentile. A clinical administration also has someone watching for rule breaks and restarting the problem, and that intervention is part of the published score; here an illegal move is simply refused and counted.

Does using the keyboard instead of tapping change my numbers?

It shifts the moving interval a little and leaves the planning interval alone. Aiming a pointer at a peg costs a hand movement that pressing 1, 2 or 3 does not, so a run answered by tapping spends slightly longer moving — but the pause before the first move is over before any of that starts. The result says how many moves arrived by tap, so you can see how much of the moving figure is travel.

You against you

What transfers from a run here is the comparison with your own next run, and the shape of your planning across problem sizes. A board the tab was hidden during is voided rather than counted as slow, and a replacement is added at the end, because the pause is the measurement and that pause contained a trip somewhere else.

This is a measurement exercise, not a clinical assessment. It reports what you did on this page against a stated reference and nothing more — it cannot establish an executive function disorder, ADHD or frontal-lobe damage. Only a qualified professional, working with more than a browser, can make that judgment.