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This problem was solved by Ali and Prateek, both from Riccarton High School in Christchurch, New Zealand, by Malcolm and Hamish, both from Madras College in St Andrews, Scotland, and by Daniella, Alice and Alice L from The Mount School in York. Jacob from SSLC and Joshua from All Saints Junior School also sent solutions.

Well done to you all - although we didn't receive any solutions that explained exactly what you had done to arrive at the answer.

Daniella, Alice L and Alice U sent this picture:

Daniella, Alice and Alice's solution.


Prateek sent us a different image of the solution:


Prateek's solution.

Ross, Brandon, Holly and Daniela from Ashford Hill Primary wrote to say:

We have found that the numbers not in use are: $3$, $6$, $14$, $20$, $22$.