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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?

Table Total

Age 14 to 16 Short Challenge Level:


In each row of the table, the third cell contains the sum of the contents of the first two cells.

In each column of the table, the third cell contains the sum of the contents of the first two cells.

What total would you get if you added up the contents of all nine cells?







This problem is adapted from the World Mathematics Championships

You can find more short problems, arranged by curriculum topic, in our short problems collection.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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