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?

30.--TWO QUESTIONS IN PROBABILITIES.

There is perhaps no class of puzzle over which people so frequently
blunder as that which involves what is called the theory of
probabilities. I will give two simple examples of the sort of puzzle I
mean. They are really quite easy, and yet many persons are tripped up by
them. A friend recently produced five pennies and said to me: "In
throwing these five pennies at the same time, what are the chances that
at least four of the coins will turn up either all heads or all tails?"
His own solution was quite wrong, but the correct answer ought not to be
hard to discover. Another person got a wrong answer to the following
little puzzle which I heard him propound: "A man placed three sovereigns
and one shilling in a bag. How much should be paid for permission to
draw one coin from it?" It is, of course, understood that you are as
likely to draw any one of the four coins as another.

31.--DOMESTIC ECONOMY.

Young Mrs. Perkins, of Putney, writes to me as follows: "I should be
very glad if you could give me the answer to a little sum that has been
worrying me a good deal lately. Here it is: We have only been married a
short time, and now, at the end of two years from the time when we set
up housekeeping, my husband tells me that he finds we have spent a third
of his yearly income in rent, rates, and taxes, one-half in domestic
expenses, and one-ninth in other ways. He has a balance of L190
remaining in the bank. I know this last, because he accident