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# Big Fish

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Age 14 to 16

ShortChallenge Level

- Problem
- Solutions

Granny caught a fish so big that she had to cut it into three pieces (head, body and tail) in order to weigh it.

The tail weighed 9kg.

The head weighed the same as the tail plus one third of the body.

The body weighed as much as the head and tail together.

How much did the whole fish weigh?

If you liked this problem, here is an NRICH task which 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.

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

The nth term of a sequence is given by the formula n^3 + 11n. Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. Prove that all terms of the sequence are divisible by 6.