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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?
Surds
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
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.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.