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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?

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.