deutsche Version

Make 24


This problem was suggested by Eva Börgens in 2002. Eva attended the 7th form of Augustinerschule Friedberg, then.

MAKE 24 is a simple game. Four figures in the range of the natural numbers 1 to 9 are chosen randomly. Your task is to combine them in order to obtain the result 24  -  but you may only use the four basic arithmetical operations and brackets.

Example:  6, 3, 6, 4  are the four numbers given.
Then  6 · 6 - 4 · 3 = 24   (you may find other solutions).

Now try:

6, 8, 9, 9

1, 3, 4, 6

3, 3, 7, 7

No ploys! Not allowed are factorials, powers, roots etc. Furthermore, you must not combine two or three of the four numbers to a two- resp. three-digit number (e.g., with 1, 3, 4, 8 given, 38 - 14 = 24 is no correct solution).


Do you need help? (But please try yourself first.) You can play MAKE 24 online:  program.

Solution

8 · 9 / (9 - 6) = 24   or   8 · (9 + 9) / 6 = 24

6 / (1 - 3/4) = 24

(3/7 + 3) · 7 = 24

The text of the problem also contained the set  1, 3, 4, 8 . There are several solutions  -  here is one of them:  4 · (8 - 3 + 1) = 24 .