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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}.

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Sixational

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Big Fish

Age 14 to 16 Short Challenge Level:

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.