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?

GEOMETRICAL PROBLEMS.

    “God geometrizes continually.”

    PLATO.

“There is no study,” said Augustus de Morgan, “which presents so simple a beginning as that of geometry; there is none in which difficulties grow more rapidly as we proceed.”  This will be found when the reader comes to consider the following puzzles, though they are not arranged in strict order of difficulty.  And the fact that they have interested and given pleasure to man for untold ages is no doubt due in some measure to the appeal they make to the eye as well as to the brain.  Sometimes an algebraical formula or theorem seems to give pleasure to the mathematician’s eye, but it is probably only an intellectual pleasure.  But there can be no doubt that in the case of certain geometrical problems, notably dissection or superposition puzzles, the aesthetic faculty in man contributes to the delight.  For example, there are probably few readers who will examine the various cuttings of the Greek cross in the following pages without being in some degree stirred by a sense of beauty.  Law and order in Nature are always pleasing to contemplate, but when they come under the very eye they seem to make a specially strong appeal.  Even the person with no geometrical knowledge whatever is induced after the inspection of such things to exclaim, “How very pretty!” In fact, I have known more than one person led on to a study of geometry by the fascination of cutting-out puzzles.  I have, therefore, thought it well to keep these dissection puzzles distinct from the geometrical problems on more general lines.

DISSECTION PUZZLES.

    “Take him and cut him out in little stars.”

    Romeo and Juliet, iii. 2.