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We received some excellent solutions to this problem. Pupils at Ysgol Aberdyfi Gwynedd wrote to tell us:
The answer we got was that there were thirty-one different numbers with digits that total the number $6$.
This is a very careful approach, well done.
Ben and Charlie from Brewood Middle School sent in exactly the same list of numbers and explained how to make sure you find all the solutions:
Well done too to Ha Young from Wesley College who also found these solutions. Children from Oakhampton Primary School decided that there are in fact thirty-two solutions because they included the single-digit number $6$ as well. Good thinking!