his wife's finger. Can you correctly answer these questions without
having the coins in sight? On which side of a penny is the date given?
Some people are so unobservant that, although they are handling the coin
nearly every day of their lives, they are at a loss to answer this
simple question. If I lay a penny flat on the table, how many other
pennies can I place around it, every one also lying flat on the table,
so that they all touch the first one? The geometrician will, of course,
give the answer at once, and not need to make any experiment. He will
also know that, since all circles are similar, the same answer will
necessarily apply to any coin. The next question is a most interesting
one to ask a company, each person writing down his answer on a slip of
paper, so that no one shall be helped by the answers of others. What is
the greatest number of three-penny-pieces that may be laid flat on the
surface of a half-crown, so that no piece lies on another or overlaps
the surface of the half-crown? It is amazing what a variety of different
answers one gets to this question. Very few people will be found to give
the correct number. Of course the answer must be given without looking
at the coins.


29.--THE BROKEN COINS.

A man had three coins--a sovereign, a shilling, and a penny--and he
found that exactly the same fraction of each coin had been broken away.
Now, assuming that the original intrinsic value of these coins was the
same as their nominal value--that is, that the sovereign was worth a
pound, the shilling worth a shilling, and the penny worth a penny--what
proportion of each coin has been lost if the value of the three
remaining fragments is exactly one pound?