# Present Buying Quiz Puzzle Answer

In the Jolly Quizmaster the other night we were talking to a chap with a large number of children and a very devious mind. He told us of a challenge that he had set his daughters when buying presents for their brothers.

He gave each daughter £8 to spend and told them:

All the presents that you buy must cost £1 or cost an exact multiple of £1.
Each of you must choose a different method of dividing your money between your brothers.
Between you, you must make sure that the total cost of each of your brothers' presents is the same.

We were amazed and asked whether his daughters had followed his instructions. Apparently they had and furthermore he gave us some extra facts:

Fiona spent more on Bobby than the other three brothers put together.
Cathy spent as much on Sam and Ricky as Fiona spent on the other two brothers.
Mary spent more on John than on any other brother.
Eve spent more on Ricky than on any other brother.
Sally is the other daughter.

We looked at each other and then asked how much each daughter had spent on each brother. He grinned, finished his pint, and said we would have to work it out for ourselves. At which point he left.

So who spent what on whom?

The first thing to do is to work out the five ways of splitting £8 into four amounts of pounds, and these are:

a) 5, 1, 1, 1
b) 4, 2, 1, 1
c) 3, 2, 2, 1
d) 3, 3, 1, 1
e) 2, 2, 2, 2

Each girl must use one of these patterns when buying the presents.

From the first fact Fiona must use pattern a, as she spends more on Bobby than the other brothers put together.

Mary and Eve must use patterns b and c (although we don't yet know which) as they spent more on one brother than any of the others.

Cathy must use pattern d, which leaves pattern e for Sally

Using the fact that each brother receives presents totalling the same amount, and putting this in a table

 Bobby John Ricky Sam By Fiona 5 1 1 1 By Cathy 1 1 3 3 By Mary (1) (4) (1) (2) By Eve (1) (2) (3) (2) By Sally 2 2 2 2 Total 10 10 10 10

Mary and Eve's totals are in brackets as we don't know which way round they are, but we know they must have spent those amounts on the four brothers.

As it happens pattern b (ie 4, 2, 1, 1) must be Mary's as she spent more on John than any of the other brothers. As thus Eve is pattern c.

Did you work it out?

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