Make 24
You will combine four numbers to reach 24 while using each once. A promising first operation may leave awkward numbers, so it helps to keep track of what remains.
- Maths
- Expert
- About 15 minutes
Help needed: yes for setup, checking and any preparation of paper or small items
What you need
- Paper
- A pencil
- The written numbers 2, 3, 5 and 7
The rule
Use every number exactly once.
How to do it
- Write the four numbers with space around them.
- Choose two numbers and an operation to combine them.
- Record the intermediate result while crossing out those used numbers.
- Combine that result with the remaining numbers one at a time.
- Check whether the completed expression equals 24.
- Check that each original number appears exactly once.
Why it works
Operations can combine the same numbers in different ways. Multiplication often makes a larger intermediate result, while addition and subtraction can adjust it. One valid expression is 7 × 3 + 5 − 2: twenty-one plus five is twenty-six, then subtracting two gives twenty-four. The order of operations matters, so multiplication is performed before the later addition and subtraction. Your final check has two parts: the value must be 24, and all four given numbers must be used once.
Make it harder
- Find a different expression with the same numbers.
- Try solving before seeing the example explanation.
- Create a new four-number set and provide a checked solution.
Ask Taz
- Why do we multiply before adding in this expression?
- Why does using a number twice break the challenge?
- Why can different expressions have the same value?
Before you start
Keep intermediate work visible so the learner can review a route that failed instead of restarting mentally. A correct total is not enough if a number was missed or repeated. Ask at dinner: “Which operation gave you a useful starting value, and which operation helped you reach exactly 24?”
Taz is an AI and can be wrong, so check what matters. Read how safety works on Taz.
Show us yours
Film your hands and what you made, not your face or name. If you are under 18, ask a parent or guardian before posting anywhere else.
Common questions
How much preparation does this need?
Use the household items above and begin with one small example. A helper can prepare the space or checking sheet while you choose the prediction. The time is an estimate and includes a little room to repeat.
What if we get different answers?
Compare the rule, the method and what each person recorded. A difference can reveal a changed assumption or an ordinary variation, so check before deciding someone must be wrong.
Do I have to share online?
No. Discuss the work at home first. Public sharing is optional and follows the privacy wording above.
More to try
See all Taz Challenges, or look through the science labs. One place for every why. Start exploring at aitaz.com