24.—­A SHOPPING PERPLEXITY.

The first purchase amounted to 1s. 53/4d., the second to 1s. 111/2d., and together they make 3s. 51/4d.  Not one of these three amounts can be paid in fewer than six current coins of the realm.

25.—­CHINESE MONEY.

As a ching-chang is worth twopence and four-fifteenths of a ching-chang, the remaining eleven-fifteenths of a ching-chang must be worth twopence.  Therefore eleven ching-changs are worth exactly thirty pence, or half a crown.  Now, the exchange must be made with seven round-holed coins and one square-holed coin.  Thus it will be seen that 7 round-holed coins are worth seven-elevenths of 15 ching-changs, and 1 square-holed coin is worth one-eleventh of 16 ching-changs—­that is, 77 rounds equal 105 ching-changs and 11 squares equal 16 ching-changs.  Therefore 77 rounds added to 11 squares equal 121 ching-changs; or 7 rounds and 1 square equal 11 ching-changs, or its equivalent, half a crown.  This is more simple in practice than it looks here.

26.—­THE JUNIOR CLERKS’ PUZZLE.

Although Snoggs’s reason for wishing to take his rise at L2, 10s. half-yearly did not concern our puzzle, the fact that he was duping his employer into paying him more than was intended did concern it.  Many readers will be surprised to find that, although Moggs only received L350 in five years, the artful Snoggs actually obtained L362, 10s. in the same time.  The rest is simplicity itself.  It is evident that if Moggs saved L87, 10s. and Snoggs L181, 5s., the latter would be saving twice as great a proportion of his salary as the former (namely, one-half as against one-quarter), and the two sums added together make L268, 15s.

27.—­GIVING CHANGE.

The way to help the American tradesman out of his dilemma is this.  Describing the coins by the number of cents that they represent, the tradesman puts on the counter 50 and 25; the buyer puts down 100, 3, and 2; the stranger adds his 10, 10, 5, 2, and 1.  Now, considering that the cost of the purchase amounted to 34 cents, it is clear that out of this pooled money the tradesman has to receive 109, the buyer 71, and the stranger his 28 cents.  Therefore it is obvious at a glance that the 100-piece must go to the tradesman, and it then follows that the 50-piece must go to the buyer, and then the 25-piece can only go to the stranger.  Another glance will now make it clear that the two 10-cent pieces must go to the buyer, because the tradesman now only wants 9 and the stranger 3.  Then it becomes obvious that the buyer must take the 1 cent, that the stranger must take the 3 cents, and the tradesman the 5, 2, and 2.  To sum up, the tradesman takes 100, 5, 2, and 2; the buyer, 50, 10, 10, and 1; the stranger, 25 and 3.  It will be seen that not one of the three persons retains any one of his own coins.

28.—­DEFECTIVE OBSERVATION.