There is a beautiful old chapel down the lane from Quiz Master Shop Towers, which has just bought new hymn books. There are lots of new hymns in these hymn books; in fact they contain 999 hymns. And this has caused a problem.
The old hymn book had far fewer hymns and thus necessitated fewer numbers to display the service's hymn numbers on the board. To tell the truth the old numbers are getting quite tatty, and new numbers are long overdue.
The hymn board takes up to three cards on each of its six rows, each with a digit from zero to nine.
How many cards of each digit does the chapel need to purchase to cater for any combination of six hymns numbers?
Consider the cards bearing digit number one. Hymn number 111 is available, and the are several hymn numbers containing two number ones. So 13 cards displaying one are needed.
And this the case for cards bearing two, three, four, five, seven and eight. So for these seven digits 13 cards are required, a total of 91.
For cards bearing the digit zero it is slightly different. No leading zeroes are shown, and there's no hymn zero; nevertheless, twelve cards bearing zero are needed.
And then we consider the digits six and nine - six is nine upside down and vice versa. So 18 cards bearing 6 or 9 are needed as all six hymns could be made up of sixes and nines.
Thus, in total, 121 digit cards are needed