Make 24

The basics

Tap a tile, tap a second tile, then tap an operator. The first tile is the left number, so 8 then 3 then minus means 8 - 3; pick 3 first for 3 - 8. The pair is replaced by its result and the merge is written above the board. Division by zero is refused and the tile shakes. Negative results and fractions are legal and are shown as they are (8/3 stays 8/3), because some hard puzzles only work through a fraction. When one tile is left it has to read 24, otherwise undo a move or restart. Hint solves the position you are actually in, not the starting position, and highlights one legal merge without playing it; when the position can no longer reach 24 it says so. Undo steps back one merge, Restart reloads the puzzle, and the arrows move between puzzles. Stars: three for a solve with no hint and no undo, two for a solve without a hint, one if you used a hint. Your best rating and time per puzzle are kept in this browser only.

Objective:

Reach exactly 24 from four numbers. Every puzzle gives you four whole numbers and asks you to use each one exactly once with plus, minus, times and divide, in any order or bracketing. One move takes two tiles, applies one operator and leaves the single result, so four numbers always take exactly three moves. There are 36 puzzles in three tiers: easy can be finished with plus and minus alone, medium needs times or divide but never leaves whole numbers, and hard cannot be solved at all without a fractional step such as 8 / (3 - 8 / 3).

Controls:

Tap (mouse, touch or pen, all handled as one tap): a tile to pick it, a second tile to pair it, an operator to apply the merge. Buttons: previous / next puzzle, Undo, Hint, Restart and Rules. Keyboard: 1 to 4 pick a tile, + - * / pick an operator, U undo, H hint, R restart, and the arrow keys change puzzle. Every button is at least 28px tall and every tile at least 40px in both axes. Add ?puzzle= to the URL to start on a puzzle number or a tier, for example ?puzzle=hard.