# The Hymn Board Puzzle

Thi is a two part puzzle that may need a notepad and calculator to work out.

A church has three hymn boards like the above and all three are used at services where hymns are sung by the congregation. The churchwarden has noticed that the metal plates with the numbers painted on are in need of replacing.

A generous church member has volunteered to pay for the new plates but she has said that the smallest number of plates must be bought at the minimum cost. You need to know that there are 700 hymns in the hymn book, and that plates are less expensive if they have a number painted on each side. Also the boards hold up to 15 plates.

The first question is how many is the smallest number of plates needed?

The second question is how much will it cost?

Each plate costs 40p to buy. Painting the numbers depends on how many identical plates are ordered. One plate with one number only costs 31p. One plate with two numbers costs 62p, two plates with two numbers each the same cost 61p each, three plates 60p each and so on (as an example, if you order 25 plates with a number on both sides, you would only pay 40p for each plate) So how much is the total cost of supplying the finished plates?