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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.

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Not Continued Fractions

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

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Coffee

To make 11 kilograms of this blend of coffee costs £15 per kilogram. The blend uses more Brazilian, Kenyan and Mocha coffee... How many kilograms of each type of coffee are used?

Symmetric Reasoning

Age 14 to 16 Short Challenge Level:



Find the sum of all the solutions of the equation $6x = \frac{150}{x}$






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