different sizes and of known dimensions. But, unfortunately, at every
one of the sixteen intersections of the cross lines a small nail has
been driven in at some time or other, and my fret-saw will be injured if
it comes in contact with any of these. I have therefore to find a method
of doing the work that will not necessitate my cutting through any of
those sixteen points. How is it to be done? Remember, the exact
dimensions of the two squares must be given.

[Illustration]

160.--THE TWO HORSESHOES.

[Illustration]

Why horseshoes should be considered "lucky" is one of those things
which no man can understand. It is a very old superstition, and John
Aubrey (1626-1700) says, "Most houses at the West End of London have a
horseshoe on the threshold." In Monmouth Street there were seventeen in
1813 and seven so late as 1855. Even Lord Nelson had one nailed to the
mast of the ship _Victory_. To-day we find it more conducive to "good
luck" to see that they are securely nailed on the feet of the horse we
are about to drive.

Nevertheless, so far as the horseshoe, like the Swastika and other
emblems that I have had occasion at times to deal with, has served to
symbolize health, prosperity, and goodwill towards men, we may well
treat it with a certain amount of respectful interest. May there not,
moreover, be some esoteric or lost mathematical mystery concealed in the
form of a horseshoe? I have been looking into this matter, and I wish to
draw my readers' attention to the very remarkable fact that the pair of
horseshoes shown in my illustration are related in a striking and
beautiful manner to the circle, which is the symbol of eternity. I
present this fact in the form of a simple problem, so that it may be
seen how subtly this relation has been concealed for ages and ages. My
readers will, I know, be pleased when they find the key to the mystery.

Cut out the two horseshoes carefully round the outline and then cut them
into four pieces, all different in shape, that will fit together and
form a perfect circle. Each shoe must be cut into two pieces and all the
part of the horse's hoof contained within the outline is to be used and
regarded as part of the area.

161.--THE BETSY ROSS PUZZLE.

A correspondent asked me to supply him with the solution to an old
puzzle that is attributed to a certain Betsy Ross, of Philadelphia, who
showed it to George Washington. It consists in so folding a piece of
paper that with