Hannah Hogben and Kelly Jane Scott of Maidstone Girls Grammar School sent solutions here with good clear explanations.

The four hymns are chosen with different numbers between 1 and 700. The board for 6 may be turned upside down to serve as a 9.

Consider first the digits 1,2,3,4 and 5. There would be the same number of boards needed for each of those digits, say xxx and xx6, xx7, xx8 where x = 1,2,3,4 or 5). Hence 9 small boards are needed for each of these digits.

For 6 (or 9) it must be possible to show 666, 669, 696 and 699 so 12 of these boards are needed.

For the 7's and 8's since 777 and 888 do not occur, it is sufficient to have 8 of each of these, for example 177, 277, 377 and 477 would use them all.

Similarly 000 does not occur so 8 zeros are needed e.g. for 100, 200, 300 and 400.

Hence the total number of boards required is 45 + 12 + 24 = 81