A group of cousins stayed for a short while with a family that lives near Quiz Master Shop Towers, and the lady of the house is a renowned baker of buns. In previous years she has struggled to keep up with the cousins' voracious appetites, so this year her husband can up with a cunning plan to try to limit bun consumption.
He offered 10p to each child for every bun eaten by the other children minus 20p for every bun eaten by that child.
When told of this, Erica said "Great, buns and money", George said "I'll never work that out!", Kate said "I bet I win the most money", and Mike simply said "Brilliant". The others said nothing, but looked thoughtful.
At the end of the stay £11.60 was paid out. All the children received some money, but none received the same amount. In addition, no child had no buns during the visit.
How many buns were eaten and in what distribution?
The amount paid out for each bun must be (n - 3) lots of 10p, where n is the number of children.
Thus the number of buns has to be 116 / (n - 3), and as the number of buns must be an integer, n can only be 4, 5, 7 or 32.
The dialogue rules out 4 and 5 children and 32 is absurd, so there must be 7 children, and 29 buns.
The only possible distribution of 29 buns between 7 children where the all have a different amount is 1, 2, 3, 4, 5, 6 and 8.