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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

Thousands of X

Age 14 to 16 Short Challenge Level:


Solve the equation $(x-2013)(x-2012)-(x-2012)(x-2011)=0.$



This problem is adapted from the World Mathematics Championships

You can find more short problems, arranged by curriculum topic, in our short problems collection.