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Amusements in Mathematics (Part 4)

Amusements in Mathematics

(Part 4)

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 setup 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 £190
remaining in the bank. I know this last, because he accidentally left
out his pass-book the other day, and I peeped into it. Don't you think
that a husband ought to give his wife his entire confidence in his money
matters? Well, I do; and--will you believe it?--he has never told me
what his income really is, and I want, very naturally, to find out. Can
you tell me what it is from the figures I have given you?"

Yes; the answer can certainly be given from the figures contained in
Mrs. Perkins's letter. And my readers, if not warned, will be
practically unanimous in declaring the income to be--something absurdly
in excess of the correct answer!


32.--THE EXCURSION TICKET PUZZLE.

When the big flaming placards were exhibited at the little provincial
railway station, announcing that the Great ---- Company would run cheap
excursion trains to London for the Christmas holidays, the inhabitants
of Mudley-cum-Turmits were in quite a flutter of excitement. Half an
hour before the train came in the little booking office was crowded with
country passengers, all bent on visiting their friends in the great
Metropolis. The booking clerk was unaccustomed to dealing with crowds of
such a dimension, and he told me afterwards, while wiping his manly
brow, that what caused him so much trouble was the fact that these
rustics paid their fares in such a lot of small money.

He said that he had enough farthings to supply a West End draper with
change for a week, and a sufficient number of threepenny pieces for the
congregations of three parish churches. "That excursion fare," said he,
"is nineteen shillings and ninepence, and I should like to know in just
how many different ways it is possible for such an amount to be paid inthe current coin of this realm."

Here, then, is a puzzle: In how many different ways may nineteen
shillings and ninepence be paid in our current coin? Remember that the
fourpenny-piece is not now current.