After a pre-Christmas carol service most of the congregation had gathered in The Jolly Quizmaster for mulled wine and mince pies, and a warm by the roaring log fire. After a while the vicar arrived too, and we fell into conversation with him. After congratulating him on a lovely service, and exchanging the usual best wishes for Christmas and the New Year, he told us about his five daughters Anne, Bridget, Carol, Diane and Elizabeth.
To buy Christmas presents for each other he had given them all £20 to spend. He had told them all to spend £1 on themselves, so they each had a small gift that they really wanted, and then to spend the other £19 on their four sisters. He further instructed them that no present for another sister was to cost less than £2 or more than £9.
Apparently all the girls complied with these instructions, and once he had checked the receipts he discovered the following facts:
- Every present had cost an exact number of pounds,
- All five daughters had received gifts (including her gift to herself) with a total value of £20,
- None of the girls had spent the same amount on any of her sisters,
- Each daughter had divided her money between her sisters in different ways,
- The most expensive present was bought by Anne for Elizabeth,
- The next most expensive gifts were Bridget's for Anne and Carol's for Diane,
- Diane spent more money on Carol than her other sisters, as did Elizabeth on Bridget,
- Diane spent the same amount on Anne as Elizabeth spent on Carol,
- Bridget and Carol spent the same amount on Elizabeth,
- Anne and Bridget spent the same amount on Diane.
We wondered who had spent what on whom, but he smiled, finished his mulled wine, and said we should be able to work it out?
So how much did each sister spend on her siblings?
The best way to approach this is with a grid filled in with the amounts spent: