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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

Relative Angles

Age 14 to 16 Short Challenge Level:

In triangle ABC, angle B is $\frac{3}{4}$ of the size of angle C and $1 \frac{1}{2}$ times the size of angle A.

What is the size in degrees of angle B?

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.