Make 24
Merge four numbers into exactly 24 with exact fractions. Practice freely, play the same Daily 5, race Sprint 60, then retry the exact states where your route died.
Use all four numbers exactly once to make 24.
Retry the state where your route died
No answer is shown first. Find any next merge that keeps at least one exact path to 24.
How difficulty & integrity workExact fractions, verified solvability, Clean vs Assisted
Every merge stays exact
Values such as 8/3 stay reduced rationals. There is no floating-point tolerance or rounded “close enough” answer.
Difficulty is structural
Easy hands have more solution routes. Standard has fewer. Challenge favors scarce routes or hands where a fractional intermediate matters.
Clean means no answer reveal
Undo and self-correction remain Clean. Check, Verified Hint and safe-merge reveal mark the active puzzle Assisted, so PBs do not mix them.
Weak Review is yours
Only puzzles where you entered a verified dead end build weak weight. Clean re-solves and clean exact-state cleanup reduce it locally.
Advanced exact route lab & custom solverAll solutions, route benchmark, adaptive drill, backup
Exact Route & Solution Lab
Inspect the original four-number hand with the same exact-rational rules used by the game. Revealing full solutions marks only the active base-game run Assisted; Custom Solver and benchmark work stay separate.
Full route reveal is assistance because it exposes the answer structure.
Exact 24 Solver & Trainer
Enter any four card values. Fractions are allowed in intermediate steps because this project keeps every value as a reduced rational instead of rounding.
Try 3, 3, 8, 8 or any four integers from 1 to 13.
Fixed Route Benchmark 20 asks which first merge preserves at least one exact path to 24. It uses the same deterministic 20 questions every clean run.
No account, remote solver, paid API, global rank, IQ score or population percentile is required. Clean 5 compares only your own repeated fixed runs on this device.