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Amusements in Mathematics

I wonder how many of my readers are acquainted with the puzzle of the "Dutchmen's
Wives"—in which you have to determine the names of three men's wives, or, rather,
which wife belongs to each husband. Some thirty years ago it was "going the rounds," as
something quite new, but I recently discovered it in the Ladies' Diary for 1739-40, so it
was clearly familiar to the fair sex over one hundred and seventy years ago. How many of
our mothers, wives, sisters, daughters, and aunts could solve the puzzle to-day? A far
greater proportion than then, let us hope.
Three Dutchmen, named Hendrick, Elas, and Cornelius, and their wives, Gurtrün, Katrün,
and Anna, purchase hogs. Each buys as many as he (or she) gives shillings for one. Each
husband pays altogether three guineas more than his wife. Hendrick buys twenty-three
more hogs than Katrün, and Elas eleven more than Gurtrün. Now, what was the name of
each man's wife?
This puzzle closely resembles the last one, my remarks on the solution of which the
reader may like to apply in another case. It was recently submitted to a Sydney evening
newspaper that indulges in "intellect sharpeners," but was rejected with the remark that it
is childish and that they only published problems capable of solution! Five ladies,
accompanied by their daughters, bought cloth at the same shop. Each of the ten paid as
many farthings per foot as she bought feet, and each mother spent 8s. 5¼d. more than her
daughter. Mrs. Robinson spent 6s. more than Mrs. Evans, who spent about a quarter as
much as Mrs. Jones. Mrs. Smith spent most of all. Mrs. Brown bought 21 yards more
than Bessie—one of the girls. Annie bought 16 yards more than Mary and spent £3, 0s.
8d. more than Emily. The Christian name of the other girl was Ada. Now, what was her
Here is an amusing little case of marketing which, although it deals with a good many
items of money, leads up to a question of a totally different character. Four married
couples went into their village on a recent Saturday night to do a little marketing. They
had to be very economical, for among them they only possessed forty shilling coins. The
fact is, Ann spent 1s., Mary spent 2s., Jane spent 3s., and Kate spent 4s. The men were
rather more extravagant than their wives, for Ned Smith spent as much as his wife, Tom
Brown twice as much as his wife, Bill Jones three times as much as his wife, and Jack
Robinson four times as much as his wife. On the way home somebody suggested that
they should divide what coin they had left equally among them. This was done, and the
puzzling question is simply this: What was the surname of each woman? Can you pair off
the four couples?