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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

Thousands of X

Age 14 to 16 Short Challenge Level:

Answer: $2012$

By factorising

Notice that the two terms have a common factor of $x-2012$, so

By expanding
Expanding both brackets and collecting like terms gives
You can find more short problems, arranged by curriculum topic, in our short problems collection.