24 Game
Make 24 from four numbers. Every puzzle is solvable and judged with exact fractions.
FAQ
Is every puzzle guaranteed solvable?
How do I type multiplication, division and two-digit numbers?
How do streaks work?
What changes on hard?
How to use
- Pick a level
Choose Normal or Hard at the top. Normal draws numbers from 1 to 10, Hard widens the range to 1 to 13 and prefers picks with fewer solutions. Changing the level deals a fresh puzzle right away, and every puzzle is solvable.
- Write the expression
Type an expression with the four numbers, plus, minus, multiply, divide and brackets. Intermediate fractions are allowed. On a touchscreen, tap the keypad below and the keys fill the input box for you.
- Submit and get judged
Press the submit button or Enter. The judge checks that each number is used exactly once and that the result is exactly 24. When something is off, the message names the exact problem.
- Use hints or skip
The Hint button shows one working expression in the status line. Skip deals a new puzzle. A wrong answer or a skip resets the streak, and the next correct answer starts counting again.
- Pause and track time
The clock starts with each puzzle and stops the moment you solve it. Pause freezes the clock, hiding the tab pauses it automatically, and coming back resumes it.
About this tool
The 24 Game is a classic arithmetic card game with a one-line rule. Take four numbers, combine them with addition, subtraction, multiplication and brackets, and make exactly 24. Every number must be used once and only once. It is usually played with a deck of playing cards, drawing only faces from 1 to 10. Four cards hit the table, and the first player to call a valid expression wins the pile. The game folds operator precedence, brackets and fraction arithmetic into one small puzzle. It feels light, but it rewards real flexibility with numbers.
This version generates, judges and hints entirely in your browser. The generator draws four numbers at random, then asks an exact fraction solver to confirm that at least one expression equals 24. On hard, it compares the number of solutions among candidate draws and deals the combinations with the fewest. Judging shares the same fraction engine. A submission passes only when every number is used once and the value is exactly 24. Nothing leaves your device, and the page keeps working offline.
How it works
Fractions are what separate casual players from strong ones. Many puzzles yield to integer steps alone, but some refuse until a fraction appears in the middle. The classic 3, 3, 7, 7 is the famous example. No integer-only path reaches 24, while 7*(3+3/7) lands exactly. A decimal check would compute 3/7 as roughly 0.4286 and end near 24.000000000000004, so a strict equality test would reject a correct answer. This site keeps every intermediate value as an integer numerator and denominator, reduced at each step. A submission passes only when the final value is exactly 24 over 1.
The solver works by reduction. Pick any two of the four numbers and combine them with one of the four operations. The problem then shrinks to three numbers, then two, then one. Divisions by zero are dropped, and commutative pairs keep a single order so the same expression never appears twice in a hint. Expressions are printed with brackets following precedence rules, so a hint can be typed straight into the input box. The generator runs the solver in reverse as an acceptor. Draws without a solution are discarded, and hard mode compares candidates by solution count before dealing the tightest one.
When to use it
- Classroom warm-up
Spend three minutes before math class on one puzzle and let the class race to answer it. Normal draws suit younger students, while hard often needs fractions and keeps older ones busy. Skip deals the next puzzle instantly, so a single lesson covers a dozen rounds.
- Playing with kids
Take turns setting puzzles for each other and award a point per correct answer. The page tracks streaks and total solves, so progress stays visible. Strict judging catches missing numbers and careless brackets, which makes it a quiet arithmetic coach.
- Fragments of waiting time
One puzzle takes about a minute, which fits a queue or an elevator ride. No account and no network are needed once the page is open. The streak reset adds a little pressure and keeps short sessions interesting. Solve one more and the counter starts climbing again.
Tips & tricks
- Look for pairs that build 24 directly, such as 4 with 6 or 3 with 8. Then see how the rest can make a 1 or a 0.
- Division often surprises. Keep a fraction in a middle step, as in 8/(3-8/3)=24.
- When you are stuck for a minute, take one step from the hint and finish the remaining three yourself.
Things to watch
- Dropping a number
The most common slip is using three numbers instead of four, or one of them twice. Look at the number cards before submitting: numbers written into the expression light up, and a dim card is still waiting to be used.
- Forgetting precedence
Multiplication and division bind first, so 8-4/2 is 6 rather than 2. Wrap anything you want evaluated first in brackets. The judge evaluates exactly what you typed, and extra brackets never hurt. A quick mental check of the order before submitting saves a wrong turn.
- Gluing digits together
A two-digit entry like 12 or 13 is only valid when that number really appears in the puzzle. Writing 13 when the puzzle holds 1 and 3 counts as a foreign number, so connect them with an operator instead. The number cards above the input always show which values are in play.