[Math Lair] The Hymn Board

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[Photograph of a hymn board]Hymn board, photograph by Anthony Easton.

During services at a certain church, there are up to five different hymns sung from the hymn book. The hymn book contains 800 hymns, numbered consecutively from 1. The hymn numbers are displayed on a hymn board by sliding in plates; each plate has digits printed on it. Each blank plate costs $1.00, and printing a digit on a plate costs 25¢. The church wants to purchase enough plates so that they are able to display every possible combination of hymns, while spending the minimum amount possible. How can they achieve the largest savings and what is the minimum amount they will have to spend?

This question is more a test of your creative thinking skills than your knowledge of advanced mathematical concepts. The answer is on the answer page. If this question seems a little difficult and you would like to try a warm-up question first, try How Many Days 'Til Christmas?.

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