You may also like

problem icon

Diophantine N-tuples

Can you explain why a sequence of operations always gives you perfect squares?

problem icon

DOTS Division

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}.

problem icon

Sixational

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.

Three Fruits

Age 14 to 16 Short Challenge Level:

Quince, quonce, and quance are three types of fruit.

7 quince weigh the same as 4 quance.

5 quance weigh the same as 6 quonce.
          
Put the fruit into order of weight, heaviest last.


Click here for a poster of this problem.

 

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.