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Age 11 to 14 Short
Challenge Level

Anastasia thinks of a positive integer.
Barry doubles Anastasia's number.
Connor trebles Barry's number.
Damion multiplies Connor's number by $6$.

Eve notices that the total of the four numbers is a perfect square.

What is the smallest positive integer that Anastasia could have thought of?

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