This problem encourages a systematic approach and it will familiarise children with number properties. 

How could you start this problem?

Why not list the square numbers/cube numbers etc?

How could you work out the median?

How about looking for squares that are listed in more that one clue to get you started? 

The problem Two and Two also requires learners to work very systematically and might be a good next step.

The hints suggest some good starting points.  Working with a partner will help many children have a go at this problem.