Make24 / Guide
Stuck? Work backwards from 24.
By Stuart Malcolm · Updated
Instead of trying random operations, look for useful shapes.
Look for factors of 24
24 is 3 × 8, 4 × 6, 2 × 12 and 1 × 24. Ask whether your four numbers can be turned into one of those pairs.
Make a useful intermediate number
A pair that becomes 2, 3, 4, 6, 8 or 12 is often worth exploring because those numbers fit 24 naturally.
Subtraction can unlock the puzzle
If two numbers are close together, their difference may give you the small factor you need.
Keep the rules in view
Every number must be used exactly once, and division must result in a whole number.
Build it in stages
With 2, 4, 6 and 8, subtract 2 from 6 to make 4. Multiply that result by the original 4 to make 16, then add 8. Look for a useful intermediate result, then work towards the target.
A quick stuck checklist
- Can one pair make 3, 4, 6, 8 or 12?
- Can two close numbers make a useful difference?
- Can an awkward number be absorbed by addition or subtraction at the end?
- Would changing the first pair open a cleaner route?