Tower of London test that separates planning from moving

The task appeared in a 1982 paper called “Specific impairments of planning”, and the title is the finding. Shallice was looking for a deficit that was not slowness, not memory and not clumsiness, in patients whose frontal damage left them fluent and capable on almost everything a clinic could measure. The tower produced it: given a target arrangement and told the minimum, the affected group did not hesitate — they reached for a bead immediately and then took far more moves than the board required. The deficit was visible only because the task has two separable costs, a pause and a sequence, and the original scoring kept them apart. That is the property nearly every browser version throws away, and it is the one this page is built around.

The board itself is smaller than it looks. Three beads on pegs holding three, two and one can only be arranged 36 ways, and from any arrangement there are between two and four legal moves — exactly three on average. That is a graph you can search exhaustively in a millisecond, which is why every minimum quoted here is a proved shortest path rather than a designer’s guess, and why the page can generate fresh problems at a stated difficulty instead of reusing a fixed set. It also puts a ceiling on the task: the longest shortest path between any two arrangements on this board is eight moves, so a twelve-problem set graded from two to six covers most of the range the geometry allows. The related puzzle that scales instead of stopping is Tower of Hanoi, where equal pegs and stacking rules make the minimum grow as 2ⁿ−1 and the interesting question becomes recursion rather than planning.

Where this version departs from the clinic is worth stating plainly, because two of the departures change what the number means. There is no examiner: in a standard administration somebody watches for a rule break, stops the participant and restarts the problem, and that intervention is part of the published score — here an illegal move is simply refused and counted, which is a different procedure with a different total. And the problems are generated rather than fixed, so no norm table applies to them; the page reports counts and intervals and never converts them into a rank. What does transfer is the comparison of you with you, and the shape of your own planning curve across problem sizes. If you want the neighboring executive measures rather than another tower, the Wisconsin card sorting test asks whether you can abandon a rule that has stopped working, the stop-signal task asks how late an action can still be cancelled, and the executive function assessment samples inhibition, switching and planning in one short run before pointing at whichever of the three you want measured properly.

A reaction time here is the interval between the frame that painted the stimulus and the timestamp the browser attached to your key, both read from the same monotonic clock. What neither can see is the display pipeline behind it, so on a 60 Hz screen roughly 16 ms of every figure below is the machine rather than you. That is the timing floor: two numbers closer together than that are the same number, and this page reports no precision it cannot support.

Both intervals on this page are hundreds or thousands of times larger than that floor, which is the one respect in which a puzzle is a kinder measurement than a reaction-time task: a frame of display latency is a rounding error against a four-second pause, so the medians are reported in whole seconds and tenths rather than milliseconds.

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.