What is the Make 24 game?
Make 24 is a mental math game where you combine four number cards from 1 to 13 with addition, subtraction, multiplication and division, using every card exactly once, to reach 24. It is often just called the 24 game, and since all it needs is a deck of cards it has long been a favourite in classrooms and at the kitchen table.
Here you pick two cards one after the other and tap an operation. The two cards fly together and turn into a new card showing the result. Four cards become three, then two, then one, and if the last card is 24 the fireworks go off and the next puzzle is dealt. Each result card carries the little expression that made it, so you can always see the path you took.
| Rule | Details |
|---|---|
| Cards | Four number cards from 1 to 13. The same number can appear more than once. |
| Operations | + − × ÷. You may use the same operation several times. |
| Use | All four cards, each exactly once. You cannot glue cards into a two digit number. |
| Order | The first card you pick goes first. Pick 8, then 2, then ÷ and you get 8 ÷ 2 = 4. |
| Fractions and negatives | Fractions and negative numbers along the way become cards too. Division by zero is not allowed. |
| Win | The last card is exactly 24. Anything else shakes and steps back one move. |
What are the most common ways to make 24?
Most solutions finish with a multiplication such as 3 × 8, 4 × 6 or 2 × 12. So the quickest start is to ask whether two of your cards can make a 3 or an 8, a 4 or a 6.
| Final step | Example cards | Solution |
|---|---|---|
| 3 × 8 | 2 · 6 · 7 · 8 | (7 − 6 + 2) × 8 = 3 × 8 = 24 |
| 4 × 6 | 2 · 3 · 5 · 6 | (5 − 3 + 2) × 6 = 4 × 6 = 24 |
| 2 × 12 | 2 · 5 · 7 · 10 | 2 × (10 + 7 − 5) = 2 × 12 = 24 |
| 24 + 0 | 4 · 6 · 9 · 9 | 4 × 6 + (9 − 9) = 24. Subtract a pair to erase it as 0 |
| 24 × 1 | 3 · 8 · 7 · 7 | 3 × 8 × (7 ÷ 7) = 24. Divide a pair to erase it as 1 |
| Fraction | 3 · 3 · 8 · 8 | 8 ÷ (3 − 8 ÷ 3) = 8 ÷ 1/3 = 24 |
| Fraction | 1 · 5 · 5 · 5 | 5 × (5 − 1 ÷ 5) = 5 × 24/5 = 24 |
How do the levels and modes differ?
There are three levels, Easy, Normal and Hard, and four modes: Practice, 3 minute run, Survival and Daily 10. Puzzles are drawn at random, and at that moment a solver walks through every possible order of operations (3,888 paths for four cards) so only solvable puzzles are dealt.
- Easy: cards 1 to 10 only, with many integer solutions that end in a multiplication.
- Normal: cards 1 to 13 that can be solved with whole numbers only.
- Hard: four in ten puzzles can only be solved through a fraction, and the rest have just a few solutions.
- Practice: no timer, and the Answer button plays the solution one step at a time.
- 3 minute run: solve as many as you can in three minutes. A hint costs 10 seconds and Skip moves on without a penalty.
- Survival: 60 seconds per puzzle. Solving refills the clock to 60, and the run ends when it hits zero.
- Daily 10: the same ten puzzles for everyone that day (3 Easy, 4 Normal, 3 Hard), with your score and time saved to the daily log.
Can four numbers always make 24?
No. Of the 1,820 possible sets of four cards from 1 to 13, 1,362 can make 24 and 458, such as 1·1·1·1 or 1·1·1·2, never can.
This game only deals solvable sets, so if you are stuck there is always another route. Sixteen of the solvable sets, including 3·3·8·8, 1·5·5·5, 1·3·4·6 and 4·4·7·7, can only reach 24 through a fraction, which makes them regulars on the Hard level.
How do Hint and Undo work?
Hint shows the next move toward 24 from the cards you have right now. The two cards to merge get the numbers 1 and 2, and the operation to use glows blue.
If you have already merged some cards, the solver runs again from that position. If 24 is no longer reachable it tells you to go back and the Undo button flashes. Undo splits the last merged card back into its two cards, and Reset brings back all four.
Tips for solving Make 24 faster
- Look for 8, 6, 4, 3 and 12 first. When you see one, check whether the other three cards can make its partner (3, 4, 6, 8 or 2).
- A pair is an eraser. Subtract it for 0 or divide it for 1 and it no longer changes the rest.
- A 1 can vanish or nudge. Multiply by it to erase it, or add it to turn 23 into 24.
- Shrink big cards. Turn 13, 12 or 11 into 12 with 13 − 1 or 11 + 1 and 2 × 12 appears.
- Stuck? Think fractions. If whole numbers fail, make a small fraction with a ÷ b and then subtract or divide.
Controls
- Phone or mouse: tap two cards, then a round operation button below. You can also tap the operation first and then two cards. Tap a picked card again to unpick it.
- Keyboard: 1 to 4 pick cards from the left, + − * / (x also multiplies), Z or Backspace undo, R reset, H hint, S answer (Practice), N or Enter skip, Esc clear the selection.
Best scores and the Practice count are stored only in this browser and are never sent to a server. The Daily 10 changes at midnight Korea time.