A coach party called into the Jolly Quizmaster last week. The tour guide has a "little arrangement" with the publican - he gets 4% commission on all the drinks bought by the passengers and by him. The commission is taken in the form of drinks.

In the pub a pint of bitter costs £5.00, a pint of mild costs £4.60 and a gin costs £5.00. There is also an offer of a "Chaser" which is a pint of bitter and a gin at a reduced price of £9.60.

This particular coach party all bought drinks that cost exactly the same amount, and the tour guide had his usual Chaser. Once all the drinks had been poured and paid for, the publican poured a half pint of bitter and gave it to the tour guide with a surreptitious wink.

How many passengers were on the coach?

The tour guide received commission of a drink worth £2.50 which is 4% of £62.50. The tour guide's purchase of a Chaser would have cost £9.60 meaning that the passengers bought drinks which cost a total of £52.90.

All of the drinks, pints, halves, shorts and offers, cost a multiple of 10 pence, so we can turn our attention to the number 529 which has factors of one, 23 and 529 - in fact it is 23 squared.

The puzzle indicates that there were passengers (plural) involved which rules out one passenger buying drinks costing the whole £52.90. Also, 529 passengers would not fit on one coach.

So we are left with 23 passengers each spending £2.30, which means all 23 of them bought half of mild.

• Quiz Master Shop

You are correct that there is an assumption that half a pint costs half the price of a pint.

• philip smith

This answer assumes that the cost of a half pint is half of a whole pint. Very often this is not the case in real life.
As the coach party spent £52.90. They cannot have bought bitter or gin(as this would be a multiple of 50p)
Hence they must have bought mild by the half pint. 23 x £2.30.