There was a good postbag for this question.

All submissions got as far as listing the possible sets of three numbers with product 72. There are 12 such "triples", namely

[1, 1, 72], [1, 2, 36], [ 1, 3, 24], [1, 4, 18],

[1, 6, 12], [1, 8, 9], [2, 2, 18], [2, 3, 12],

[2, 4, 9], [2, 6, 6], [3, 3, 8] and [3, 4, 6].

But what about the door number? How does Mrs Smith's answer help Sally?

This part of the solution was a stumbling block for many entrants.

We assume that Sally knew the number. Now all the triples have a different sum EXCEPT [2,6,6] and [3,3,8] which both sum to 14. So the door number must be 14, otherwise the information would have told Sally the answer. It follows that the correct triple must be one of these two.

Finally, since Amanda is the youngest child, she is not a twin, and the correct triple is [2, 6, 6] rather than [3, 3, 8], so we know that Mrs Smith has a 2 year old called Amanda and twins aged 6.

There were many partially correct solutions and plenty of correct answers with explanations that were incomplete or plain false, but solutions from the following were both complete and correctly argued.

Jessica Huntley, Daniel Roberts and Mark Wang of Jack Hunt School, Peterborough;

Alice Lewin, Ashley Holmes, Alice Unwin and Elisabeth Elvidge of The Mount School, York;

Larissa Hansford, Hollie Jefferson and Emma Titterington, also of The Mount School;

Rachel Walker and Christiane Eaves, again of The Mount School;

Georgina Baxter of Davison High School, Worthing;

Rosie Johns of Davison High School, Worthing;

James Page of Hethersett High School.