But even after these points are all seen there comes in a new difficulty:  for although it will be found that all the 8’s may be on the backs of the 7’s, we cannot have all the 2’s on the backs of the 1’s, nor all the 4 on the backs of the 3’s, etc.  There is a great danger, in our attempts to get as many as possible painted alike, of our so adjusting the figures that some particular combination of hymns cannot be represented.

Here is the solution of the difficulty that was sent to the vicar of Chumpley St. Winifred.  Where the sign X is placed between two figures, it implies that one of these figures is on one side of the plate and the other on the other side.

d.    L s.  d.
31 plates painted 5 X 9 @  41/2 = 0 11  71/2
30       "        7 X 8 @  43/4 = 0 11 101/2
21       "        1 X 2 @  7  = 0 12  3
21       "        3 X 0 @  7  = 0 12  3
12       "        1 X 3 @  91/4 = 0  9  3
12       "        2 X 4 @  91/4 = 0  9  3
12       "        9 X 4 @  91/4 = 0  9  3
8       "        4 X 0 @ 101/4 = 0  6 10
1       "        5 X 4 @ 12  = 0  1  0
1       "        5 X 0 @ 12  = 0  1  0
149 plates @ 6d. each         = 3 14  6
----------
L7 19  1

Of course, if we could increase the number of plates, we might get the painting done for nothing, but such a contingency is prevented by the condition that the fewest possible plates must be provided.

This puzzle appeared in Tit-Bits, and the following remarks, made by me in the issue for 11th December 1897, may be of interest.

The “Hymn-Board Poser” seems to have created extraordinary interest.  The immense number of attempts at its solution sent to me from all parts of the United Kingdom and from several Continental countries show a very kind disposition amongst our readers to help the worthy vicar of Chumpley St. Winifred over his parochial difficulty.  Every conceivable estimate, from a few shillings up to as high a sum as L1,347, 10s., seems to have come to hand.  But the astonishing part of it is that, after going carefully through the tremendous pile of correspondence, I find that only one competitor has succeeded in maintaining the reputation of the Tit-Bits solvers for their capacity to solve anything, and his solution is substantially the same as the one given above, the cost being identical.  Some of his figures are differently combined, but his grouping of the plates, as shown in the first column, is exactly the same.  Though a large majority of competitors clearly hit upon all the essential points of the puzzle, they completely collapsed in the actual arrangement of the figures.  According to their methods, some possible selection of hymns, such as 111, 112, 121, 122,211, cannot be set up.  A few correspondents suggested that it might be possible so to paint the 7’s that upside down they would appear as 2’s or 4’s; but this would, of course, be barred out by the fact that a representation of the actual figures to be used was given.