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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

Well Read

Age 14 to 16 Short
Challenge Level

In Miss Quaffley's class, one third of the pupils take a teddy bear to school.

Last term, each boy borrowed 12 books from the library, each girl borrowed 17 books, and each teddy bear borrowed 9 books.

In total 305 books were borrowed.

How many girls are there in the class?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

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