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Not Continued Fractions

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

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Coffee

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Table Total

Age 14 to 16 Short Challenge Level:

In each row of the table below, the number in the third column is the sum of the numbers in the first two columns.

In each column of the table, the number in the third row is the sum of the numbers in the first two rows.

What is the sum of all of the numbers in the table?

4  + 4
8  + 8
 + 8  + 4 16

 



This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.