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(w)holy Numbers

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A church hymn book contains 700 hymns, numbered 1 to 700.

Each Sunday the people in the church sing four different hymns.

The numbers of the hymns are displayed to them in a frame by dropping in single-digit boards like this:

number 2

The board for 6 may be turned upside down to serve as a 9.

What is the minimum number of small boards that is needed to show any possible combination of four hymn numbers?

How many of each number must there be?

hymn board



Click here for a poster of this problem.