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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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Oldest and Youngest

Age 14 to 16 Short Challenge Level:


Edith had nine children at regular intervals of $15$ months.

If the oldest is now six times as old as the youngest, how old is the youngest child?


If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.