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Always Two

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

Not Continued Fractions

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


Find the exact values of x, y and a satisfying the following system of equations: 1/(a+1) = a - 1 x + y = 2a x = ay

Square to a Rectangle

Age 14 to 16 Short
Challenge Level

Kevin had some square patio tiles which he arranged to make a square.

He decided to change it into a rectangle by making one of the sides 3 tiles shorter, and the other side 4 tiles longer.

To make this change, Kevin only needed to buy one extra tile.

What are the lengths of the sides of the rectangle?

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