The Jolly Quizmaster has started selling cigars, and there are three brands selling at £1.00, £1.50 and £2.00. The other evening we asked the landlord how sales were going and he imparted the following.
A group of brothers had come into the pub and all spent £20 on cigars. All the brothers had bought twelve cigars, but none of them had bought the same combination of cigars. And afterwards the landlord had worked out that there were no other possible combinations of twelve cigars totalling £20.
How many of the three brands did the brothers buy between them?
You can work out the combinations as follows:
Four at £2.00 and eight at £1.50
Five at £2.00, six at £1.50 and one at £1.00
Six at £2.00, four at £1.50 and two at £1.00
Seven at £2.00, two at £1.50 and three at £1.00
Eight at £2.00 and four at £1.00
There were five brothers (although we did not ask that) who bought 30 cigars at £2.00, 20 cigars at £1.50 and ten cigars at £1.00.