BoardSolve
All games
🕵️

Deduction

Guess Who?

Information-theoretic half-split solver.

2 players1 solverSolved
HeuristicBest moveProbabilities
Character board
Click a tile to cross it out or bring it back. Manual toggles always win, so any homemade question (“looks like the maths teacher”) works fine — just eliminate the tiles yourself.
24 / 24 live
Optimal question
Greedy half-split — the information-theoretic optimum for binary questions. Highlighted tiles above show who would answer YES.

Press Recompute to get a suggestion.

  • Information lower bound: at least ⌈log₂ 24⌉ = 5 more questions needed in the worst case.
  • Early game: prioritise questions that split the board cleanly in two.
Compound question
Combine any number of feature clauses with AND / OR (and optional NOT). The compound question is ranked alongside the built-ins so you can see immediately if it splits the live set better.

No clauses yet. Add one to build a question like “bald AND wearing glasses” or “blond hair OR red hair”.

Deep dive

How BoardSolve plays Guess Who?

Guess Who? is a 24-character deduction game where every legal question partitions the candidate set into two. The worst-case-optimal strategy is to pick the question whose partition is as close to a 50/50 split as possible — a result that follows from a simple adversary argument.

Why half-split is optimal

For any binary question that splits N candidates into groups of size a and b = N − a, the adversary can always answer to leave you with max(a, b) candidates. Minimising max(a, b) over the question set is exactly the greedy half-split rule, and a straightforward induction shows it is optimal for the whole game tree (not just one turn).

BoardSolve ranks every encoded question by worst-case eliminations and surfaces ties so you can pick the one that's easiest to phrase out loud. A manual toggle lets you mark characters eliminated by homemade questions the engine can't encode.

References & further reading

  1. Hyafil, L. & Rivest, R. L. (1976) . Information Processing Letters 5(1), 15–17Hardness of optimal decision trees in general — motivates the greedy half-split heuristic.
  2. Garey, M. R. (1972) . SIAM Journal on Applied Mathematics 23(2), 173–186Foundational result on greedy half-split for identification problems.
  3. Shannon, C. E. (1948) . Bell System Technical Journal 27, 379–423Source of the entropy bound on the number of binary questions needed.