# Puzzle page

Issue 14
in
March 2001

## 3 3 8 8 puzzle

Using the four numbers 3, 3, 8, and 8, and the usual four arithmetic operations (addition, subtraction, multiplication and division), can you make the number 24?

This looks a bit too easy (3 × 8 = 24), until I tell you that you have to use all four numbers - both 3s and both 8s. No silly tricks allowed - you can't use an 8 and a 3 to make 83, or raise numbers to powers or take square roots or factorials or anything else of that kind.

You can use fractions on the way, of course, but the final answer must be exactly 24. For example: 3 × 8 + (3/8) makes 24 and three-eighths, which is quite close, but no banana.

You can send your solution by e-mail to <plus@maths.cam.ac.uk>.

For some challenging mathematical puzzles, see the NRICH puzzles from this month or last month.

We have received a couple of correct solutions to the PLUS issue 13 puzzle. If you don't want to keep trying it yourself, you can see how it's done.

### 3388 puzzle

Divide the first 3 by itself (Not another digit) that equals 1 plus the next digit 3 = 4 times 8 = 32 minus 8 = 24.

### This is wrong because you

This is wrong because you have already used 3 three times. Duh!

8/(3-(8/3))
8/((9-8)/3)
8/(1/3)
24

### Another one not that easy

How to make 21 with 1, 5, 6 and 7?

6 / (1 - 5 / 7)
= 6 / (2 / 7)
= 6 * (7 / 2)
= 21