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**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

last update 2006-04-10

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