24.—­A shopping perplexity.

Two ladies went into a shop where, through some curious eccentricity, no change was given, and made purchases amounting together to less than five shillings.  “Do you know,” said one lady, “I find I shall require no fewer than six current coins of the realm to pay for what I have bought.”  The other lady considered a moment, and then exclaimed:  “By a peculiar coincidence, I am exactly in the same dilemma.”  “Then we will pay the two bills together.”  But, to their astonishment, they still required six coins.  What is the smallest possible amount of their purchases—­both different?

25.—­Chinese money.

The Chinese are a curious people, and have strange inverted ways of doing things.  It is said that they use a saw with an upward pressure instead of a downward one, that they plane a deal board by pulling the tool toward them instead of pushing it, and that in building a house they first construct the roof and, having raised that into position, proceed to work downwards.  In money the currency of the country consists of taels of fluctuating value.  The tael became thinner and thinner until 2,000 of them piled together made less than three inches in height.  The common cash consists of brass coins of varying thicknesses, with a round, square, or triangular hole in the centre, as in our illustration.

[Illustration]

These are strung on wires like buttons.  Supposing that eleven coins with round holes are worth fifteen ching-changs, that eleven with square holes are worth sixteen ching-changs, and that eleven with triangular holes are worth seventeen ching-changs, how can a Chinaman give me change for half a crown, using no coins other than the three mentioned?  A ching-chang is worth exactly twopence and four-fifteenths of a ching-chang.

26.—­The junior clerk’s puzzle.

Two youths, bearing the pleasant names of Moggs and Snoggs, were employed as junior clerks by a merchant in Mincing Lane.  They were both engaged at the same salary—­that is, commencing at the rate of L50 a year, payable half-yearly.  Moggs had a yearly rise of L10, and Snoggs was offered the same, only he asked, for reasons that do not concern our puzzle, that he might take his rise at L2, 10s. half-yearly, to which his employer (not, perhaps, unnaturally!) had no objection.

Now we come to the real point of the puzzle.  Moggs put regularly into the Post Office Savings Bank a certain proportion of his salary, while Snoggs saved twice as great a proportion of his, and at the end of five years they had together saved L268, 15s.  How much had each saved?  The question of interest can be ignored.

27.—­Giving change.