Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some other
possibilities for yourself!
Can you explain the strategy for winning this game with any target?
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
This part of the solution was a stumbling block for many
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
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
Jessica, Daniel and Mark of Jack Hunt School, Peterborough;
Alice, Ashley, Alice and Elisabeth of The Mount School,
Larissa, Hollie and Emma, also of The Mount School;
Rachel and Christiane, again of The Mount School;
Georgina of Davison High School, Worthing;
Rosie of Davison High School, Worthing;
James of Hethersett High School.