the bean climbing spirally as at A above, whereas the French bean, or
scarlet runner, the variety clearly selected by the artist in the
absence of any authoritative information on the point, always climbs as
shown at B. Very few seem to be aware of this curious little fact.
Though the bean always insists on a sinistrorsal growth, as B, the hop
prefers to climb in a dextrorsal manner, as A. Why, is one of the
mysteries that Nature has not yet unfolded.
426.--THE HYMN-BOARD POSER.
This puzzle is not nearly so easy as it looks at first sight. It was
required to find the smallest possible number of plates that would be
necessary to form a set for three hymn-boards, each of which would show
the five hymns sung at any particular service, and then to discover the
lowest possible cost for the same. The hymn-book contains 700 hymns, and
therefore no higher number than 700 could possibly be needed.
Now, as we are required to use every legitimate and practical method of
economy, it should at once occur to us that the plates must be painted
on both sides; indeed, this is such a common practice in cases of this
kind that it would readily occur to most solvers. We should also
remember that some of the figures may possibly be reversed to form other
figures; but as we were given a sketch of the actual shapes of these
figures when painted on the plates, it would be seen that though the 6's
may be turned upside down to make 9's, none of the other figures can be
so treated.
It will be found that in the case of the figures 1, 2, 3, 4, and 5,
thirty-three of each will be required in order to provide for every
possible emergency; in the case of 7, 8, and 0, we can only need thirty
of each; while in the case of the figure 6 (which may be reversed for
the figure 9) it is necessary to provide exactly forty-two.
It is therefore clear that the total number of figures necessary is 297;
but as the figures are painted on both sides of the plates, only 149
such plates are required. At first it would appear as if one of the
plates need only have a number on one side, the other side being left
blank. But here we come to a rather subtle point in the problem.
Public-domain text, read in full here on John Shaqi.
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