How Make 24 works
The idea is old and simple: four numbers, the four basic operations, and a target of 24. Teachers have used it for decades because it turns arithmetic into a puzzle with a clear finish line. It is also a good daily workout for adults, since a hand takes anything from five seconds to a few stubborn minutes.
In Make 24 you play with cards instead of writing sums. Tap a card, tap an operator, then tap another card, and the two cards merge into one that shows the result. Four cards become three, then two, then one. If that last card says 24, the hand is yours. Made a wrong turn? Undo goes back one step, and Reset puts all four cards back.
Three ways to play
Practice has no clock. Use Hint when you are stuck and it lights up the first step of a solution. Skip deals a new hand and shows you one answer to the hand you left, so you still learn something from it.
Sprint gives you 60 seconds. Every solved hand scores a point, and your best score for Easy and Hard is saved on this device. Sprint never deals the fraction puzzles, so it rewards speed rather than one brutal hand.
Daily 5 is the same five hands for everyone, every day. The first three are friendly, the fourth uses cards from 10 to King, and the last one needs a fraction. Your time is the score.
Worked examples
1 2 3 4. The friendliest hand there is. 1 × 2 = 2, 2 × 3 = 6, 6 × 4 = 24. Multiplying everything works here, but that is rare.
4 7 8 8. Look for 3 × 8 and you will not find a 3. Try 4 × 6 instead: can 7, 8 and 8 make 6? 8 ÷ 8 is 1, and 7 − 1 is 6. So the answer is 4 × (7 − 8 ÷ 8). There are other ways too, such as 8 × 7 − 8 × 4, which is 56 − 32.
1 5 6 6. The 30 − 6 pattern: 5 × 6 = 30, then 30 − 6 = 24, and the 1 multiplies the result without changing it.
J Q K 1 (11 12 13 1). Face cards look scary, but 13 − 11 = 2 and 12 × 2 = 24. Multiply by the 1 at the end and you are done.
3 3 8 8. The famous one. Nothing whole works, and the only solution goes through a fraction. Divide 8 by 3 to get 8/3. Take that away from 3: 3 − 8/3 = 1/3. Now divide the other 8 by 1/3, which is the same as multiplying by 3, and you get 24. Written out: 8 ÷ (3 − 8 ÷ 3).
1 5 5 5. Another fraction hand. 1 ÷ 5 = 1/5, 5 − 1/5 = 24/5, and 5 × 24/5 = 24.
Getting faster
Good players do not try every combination. They look at the cards and ask which of a handful of endings could work: 3 × 8, 4 × 6, 2 × 12, 30 − 6, 20 + 4 or 48 ÷ 2. Then they check whether the other cards can build the missing piece. After a few dozen hands this becomes automatic, and you start seeing 24 almost as soon as the cards land.
Big cards are easier to tame than they look. A 12 wants a 2, a 13 often pairs with an 11 to make 2, and a 10 likes to become 10 + 10 + 4 or (10 × 10 − 4) ÷ 4. Small cards and doubles are where hands hide their tricks, because the obvious moves run out.
When you get stuck, change the question. Instead of “how do I make 24 from four cards”, ask “what do these three cards need to make next to the fourth one”. That smaller question is usually easy.
Using the 24 solver
The Solver button opens the 24 solver over the game. Type any four numbers from 1 to 13 and press Solve to see every distinct way to make 24, with answers that only swap the order of a sum or a product listed once. If there is no way, it says so. It opens with the current hand filled in, which makes it handy for checking an answer after a hand you skipped, or for settling an argument over a deck of cards at the kitchen table.
If you enjoy number puzzles like this, try Mental Math for speed, Calcudoku for arithmetic logic grids, or Kakuro for sums in a crossword.
How to play Make 24
- You get four number cards. Use each card exactly once, with addition, subtraction, multiplication and division, to make 24.
- Tap a card, tap an operator, then tap a second card. The two cards merge into one new card that shows the result. Keep going until one card is left.
- If the last card is 24, you win the hand. Fractions are allowed along the way, so 8 ÷ 3 makes a card that reads 8/3.
- Undo takes back your last step and Reset brings back all four starting cards.
- Easy deals cards from 1 to 9. Hard deals cards from 1 to 13, with J = 11, Q = 12 and K = 13, and includes the puzzles that need fractions.
- Practice has no timer, a Hint button and Skip. Sprint gives you 60 seconds to solve as many hands as you can. Daily 5 is the same five hands for everyone today, timed.
- Every hand we deal has at least one solution.
Make 24 tips
Look for the four big pairs
Most hands end with one of a few moves: 3 × 8, 4 × 6, 2 × 12 or 30 − 6. Scan your cards for one half of a pair, then ask whether the other two cards can build the other half. With 6, 9, 3, 2 you can keep the 6 and make 4 from 9 − 3 − 2, then 6 × 4.
Work backwards from 24
Pick one card and ask what the other three need to make. Holding an 8, you need 3 (for 8 × 3), 16 (for 8 + 16) or 32 (for 32 − 8). Three cards making a small target is much easier than four cards making 24.
Use division to make fractions
When nothing whole works, divide. 8 ÷ 3 looks useless, but 3 − 8/3 is 1/3, and 8 ÷ 1/3 is 24. The hardest hands can only be solved this way.
Turn a 1 into a free pass
A 1 can multiply or divide anything without changing it, so 1 lets you solve the other three cards and then tidy it away. Two equal cards work the same way: 7 − 7 makes 0 and 7 ÷ 7 makes 1.
Frequently asked questions
How do you play the 24 game?
You get four numbers and must combine all of them with +, −, × and ÷ to reach exactly 24, using each number once. In Make 24 you tap a card, an operator and a second card, and the two cards merge into their result. When the last card shows 24, the hand is solved.
Is every 24 game hand solvable?
No. Of the 1,820 different hands you can make from four cards between 1 and 13, 1,362 can make 24 and 458 cannot. Hands like 1 1 1 1, 1 1 1 2 or 6 6 9 9 have no answer. Make 24 only deals solvable hands, and the solver tells you when a hand you type in has no solution.
What are the hardest 24 puzzles?
The hardest ones need a fraction along the way. 3 3 8 8 has only one answer, 8 ÷ (3 − 8 ÷ 3). 1 5 5 5 is solved by 5 × (5 − 1 ÷ 5), and 1 3 4 6 by 6 ÷ (1 − 3 ÷ 4). There are 16 hands like this with cards up to King, and they show up in Hard mode and as the last hand of Daily 5.
How does the 24 solver work?
Open Solver, type any four numbers from 1 to 13 (A, J, Q and K work too) and press Solve. It tries every order, operator and grouping with exact fractions, then lists each distinct solution once. Answers that differ only in order, like 3 × 8 and 8 × 3, count as one.
Can I use negative numbers or fractions?
Yes. Any step is allowed as long as you use every card once and finish on 24. Fractions show on the card as a/b. You never need a negative number to solve a hand, but you can make one if it helps you think.
Is this the official 24 game?
No. 24 Game is a trademark of Suntex International, which makes the classroom card version. Make 24 is our own free version of the same classic number puzzle.
