SOLUTIONS
showing how this placing of the figures may be done than by the
doing of it. Therefore have I in suchwise written the numbers that
they do add up to twenty and three in all the twelve lines of three
that are upon the butt."
I think it well here to supplement the solution of De Fortibus with
a few remarks of my own. The nineteen numbers may be so arranged
that the lines will add up to any
number we may choose to select
from 22 to 38 inclusive, except-
ing 30. In some cases there are
several different solutions, but in
the case of 23 there are only two.
I give one of these, and leave the
reader to discover the other for
himself. In every instance there
must be an even number in the
central place, and any such num-
ber from 2 to 18 may occur.
Every solution has its comple-
mentary. Thus, if for every
number in the accompanying
drawing we substitute the differ-
ence between it and 20 we get
the solution in the case of 37.
Similarly, from the arrangement
in the original drawing, we may at once obtain a solution for the
case of 38.
36.—
The Donjon Keep Window.
In this case Sir Hugh had greatly perplexed his chief builder by
demanding that he should make a window measuring one foot on every
side and divided by bars into eight lights, having all their sides equal.
The illustration will show how this was to be done. It will be seen
that if each side of the window measures one foot, then each of the
eight triangular lights is six inches on every side.
" Of a truth, master builder," said De Fortibus slyly to the
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