"NUTS!"

Evening Post, Volume CXX, Issue 155, 28 December 1935, Page 15

"NUTS!"

Intellect Sharpeners All rights reserved

(By C. J. Wherefore)

Readers with a little Ingtruilty will find in this column an abundant stars of entertainment and amusement, and tho salving of the problems should provide excellent mental exhilaration. While some of the "nuts" may appear harder than others, It will be found that none will require a sledgehammer to crack them. Address corresllMimi to P.O. Box 1177, Welllnitta.

THE ART OF SELLING.

"You see these little steel rules," said the storekeeper,- "we sell them for so much ■ over the counter," and here he mentioned the price. "A hawker buys them from us, arid sells them over the doorstep for three and one-third times our price. If his intended victims show signs of bargaining, he reduces his demands by twothirds of our price, but even then he makes a profit of .one. shilling and three pence. Good salesmanship, isn't it, or would you call it by'a less complimentary , name?". At what, prices (are these goods sold by the shopkeeper and by the hawker? A SEASONABLE PROBLEM. The following may be considered appropriate as a ■ Christmas problem published in this country, but -would be regarded as not true to description in some other parts of the Empire. Mr. M: Neil,,who is a grower of roses, and very proud of them, borrowed a basket from, .his next-door neighbours, and when he returned it, he filled it with his best specimens,', red, white, and pink. He had picked equal numbers of the red ,and pink ones, but he found he had more than the basket -would hold, •so he rejected; a few, and the result was that he had given his friends 4 pink.roses with every 3.red ones. The basket held just i 100 altogether. There were three daughters in the family next door, and they were delighted with the flower^. The eldest, who seems to have been rather a selfish girl, -appropriated all there were of one particular colour. The second one, who may have been a'little less-unamiable, took'all there were of another colour." Her consolation was that she had a great deal more than her sister; if she had found five more in the basket, her portion would have been twice as numerous as the other. There remained only roses of one colour, 'and Cinderella was allowed to have them. Although she did not tell her. sisters, she was pleased to find that these were r of the colour she especially likes. What colour among roses is Cinderella*s favourite? THREE BALES OF WOOL. The man employed in a wool store to weigh the bales, had just handled three with the same brand. None of them came to 400 pounds, and the numbers he wrote in his book 'vised all the numerals from'l to 9,: but. none of them more than once. The difference between the heaviest and lightest was the maximum that was possible. The bale of medium weight contained fleeces of which the average weight was more than 8 pounds. How many fleeces did this bale contain? For the purpose of the problem the weight of the wool pack is disregarded, and fractions of pounds are not used. SUBSTITUTION. The following problem is intended to be solved by armchair methods. The line represents an, entry on an invoice, in which A, B, C, D, are consecutive numbers, of which Ais the least. N is not a whole number; it consists of a number with an additional fraction, such that there-is-a half-inch in the quantity measured off. N yards';'at A pence, £B Cs Dd. ' A CHRISTMAS PROBLEM. Those- enthusiastic problemists, the three members of the family of Brown, are uhable this Christmas to supply examples of the ingenuity of each one of them considered separately. Their explanation is that they ■ decided to collaborate, and after devising one problem, they found that their supply of imagination had come to an end. The masterpiece they have sent, deals with the experiences of four men, A. B;.C; and D, whose.wives are-M, N, O, and P, not necessarily respectively. The husbands go to one department to buy presents for their wives, and the wives go to another to purchase for their husbands. The problem is to find which are the married pairs. The three collaborators were unable to agree about the clues to be offered, and the only plan seemed to be that each one should give his own idea in a follpw-my-leader fashion, and the question of finding whether a solution is possible should be postponed .until all particulars were collected. The following is.the result. All presents cost shillings withoutadditional pence. A, who is hard up, spends a smaller amount than any other man, and his expenditure is five shillings less than that of B. M, who is not A's wife, is also very short of cash,-and spends less than any other woman; her expenditure is five shillings less than that of- N. One husband spends four times as much as one other husband, and one wife spends four times as much as one other wife. Altogether the men spend £4, and the women £3. It was at this point that the members of the league'began to dis^ agree. Arthur had: suggested that the differences between the sums spent by each man and by his own wife were always 10 shillings or a multiple of 10, and this was accepted by the others, but not altogether willingly. Geoffrey proposed to vary the-procedure by saying that only three of them differed by this amount, the fourth one being an exception. To this Miss Brown retorted that it made the problem impossible. .'Then she took her remark back, land.smiled as if much amused, but.in reply to questions as to what she was laughing at she merely urged her two brothers to solve the problem' and find out. Which-are the married pairs in these eight individuals, and wnats was the cause of Miss B's. amusement? SOLUTIONS. Ages.—The brother's : age is inevitably 18, but the other ages are not ascertainable. Time.—The train left at one minute before 12, midday, which is a.m. time, but comes very near to being otherwise. Samples.—The number posted the first, day was 132, because ho other multiple of 12 will fit. This was increased by- 23 each succeeding day, until in 8 days he had sent away 1700 samples. Armchair Problems.—(l) The taxi fare was one shilling, and the cheque was for £17, because it is clear that he had one penny hi addition to: the remaining shillings: Other solutions exist, but they. are not, of a kind that armchair specialists are likely.to discover. (2) The first payment must have been 3d, because there is no solution, with 1 or 2 pence. But With this amount there are many solutions, so that the price of the ball must remain unknown, and is not asked for. Bequest.—The difficulty at first seems to be that there are too many solutions. But several of these arc rejected at once, for instance 18 families, each of one child, because they are contrary to the terms- of the bequest. Others, which involve families of 23 or even more children, are discarded as contrary to natural laws;-and the result is that only two-possibilities are left, namely, 11 families o£ 8,; and 9 families, of 12, so these must be. the numbers which/received' subsidies'in the twoyears mentioned.