Edmund's Brainteasers
Problem 20
Solution
Problem 20: The Concert. Solution.
Consider the fourth Sunday. If they had x tickets to sell that day and they sold 6x/7 + 1/7 tickets then, since they have none left, this must equal x. Solving 6x/7 + 1/7 = x gives x = 1. Now consider the second last Sunday. If they start with x tickets, sell 6x/7 + 1/7 and have 1 left then 6x/7 + 1/7 = x - 1. This gives x = 8. Similarly for the third last Sunday, 6x/7 + 1/7 = x - 8 so x = 57. Finally, for the first Sunday, 6x/7 + 1/7 = x - 57 so x = 400. The Vestry must have started with 400 tickets which they sold at £5 each, making £2000 towards the heating.