NUTS TO CRACK.

Otago Witness, Issue 3885, 28 August 1928, Page 69

NUTS TO CRACK.

By

T. L. Briton.

(For the Otago Witness.) Readers with a little ingenuity will find in ds column an abundant ■tore of entertainmet ’ and amusement, and the solving of the prob--leni« übculd provide excellent mental exhilaration While some of the “nuts' may appeal harder than others, It will be found that none will require a sledge-hammer to crack them. Solutions will appear in our next Irrnue together with some fresh aute.’ Readers re requested not to send in their solutions, unless these are ■p-rcially asked for, but to keep them for comparison with those published in the Issue following the publication of the problems. CHANGE OF A SOVEREIGN IN SILVER. If, as has been correctly stated, a person may have as much as 15s 9d in current New Zealand silver coin without being able to change exactly a 10s note, can the reader say what are the fewest silver coins he can hold which will represent the difference between twice 15s 9d and the maximum amount in New Zealand silver coins that he can have without being able to give the exact change for twice the sum mentioned which could not be changed by a person holding current silver to the amount of 15s 9d? I’he reader would no doubt be able to construct this sentence in a much clearer form, even if two sentences are made of it, but in extenuation it must not be forgotten that this is an intellect sharpening column 0 THE COAL MERCHANT. A coal merchant received a cheque from a steam laundry company with the instructions that it was to be “ wholly expended equally in-the supply of two classes of coal.” and as the prices, viz., £3 and £4 per ton respectively—had been agreed upon, the laundry manager knew what quantity he should receive of each. But when the coal arrived it was found short weight by exactly half a ton, counting the two lots together Upon inquiry it was found that the merchant had wrongly read the instructions, which, however, were not very clear, and delivered equal quantities of both grades to the full value of the cheque, instead of apportioning one half the sum for one grade and the other half for the supply of the better quality. VVhen the matter was further looked into it was quickly seen that if the order had been fulfilled as the laundry people intended, another half ton should have been delivered as stated. To find, from these particulars, the amount of the cheque sent, will give the reader an exfacuJties ChanCe U exerdse his me »tal A PECULIAR OCCURRENCE. A corespondent signing himself “ Auction Bridge ” writes asking an explana tion of a paradox that appeared in this column some time ago, as he saw no solution of the curious happening. It is concerning four men who sat down one night to play for money, and, although they tended ■> stop at midnight, played on till nearly daybreak. “There !S nothing very peculiar about that part of it, he writes; “but the thing that puzzles us is that when accounts were being squared up next day (for no money was produced during the playing), every one of the four was a gainer pecuniarily, the only thing lost being their night’s rest. _ Can the reader enlighten “ Auction Biidge on this peculiar occurrence for there was no “pool” on the table from which the players could draw when winning, neither was there any dividend paying machine or other device, only the four men mentioned taking part? The writer of these notes is under the impression that the paradox was explained under the heading “ Answers to Correspondents.” but may be wrong.

AN ARMCHAIR PROBLEM. .Problems not infrequently appear in this column which are intended to be solved without the use of pencil and paper, and, if so treated, are apt to sharpen the intellect equally with those that require the several stages of solving to be written down. One of this variety which appeared last month formed the subject of discussion at more than one fireside, and in one instance the oldest boy in the family, a lad of 14, afterwards told his schoolmate that it “ fairly floored the pater.” Well, here is another which may be called an “ armchair problem.” If a train travelling at 30 miles an hour overtakes another train of the same length travelling on a parallel line and completely passes it in one -minute, at what rate was No. 2 train travelling if next day No. 1 met No. 2 going in the opposite direction, both travelling uniformly at the same speeds as the day before, and passed it completely in 20 seconds? This “nut” should give the reader a few moments of thinking, but he should be able to determine the correct speed in a little time without the use of pencil and paper. AN EXCHANGE OF LANDS. An exchange of lands held by two graziers was effected. recently, the particulars of which offer material. for/ a useful problem. Mr” Jones owned -a square block of land which we WilPeAll “A,” situated too far' away from his

homestead to be economically worked, but within easy distance of his neighbour’s woolshed. The. latter (Mr Brown) was in somewhat the same predicament, for he had two smaller blocks separated from one another across the creek and quite handy to Jones’s paddocks. One of these blocks was also in the form of a square, and the other was oblong in shape. They may be called B and C respectively. As the area of A was approximately equal to B and C combined, and the values per acre of the three on a par, the two graziers effected an exchange. Now, the problem is to find how much more fencing one had to erect than the other on the boundaries of their new possessions, for the three blocks were open country, the only details available being that one side of A was the same length as the long side of C, a side of B being equal to the short side of C, and also that the three blocks combined contained 122 J acres, while A and B together had an area of 85 acres. This will be found both a useful and interesting calculation. LAST WEEK’S SOLUTIONS. WHEN CAPTAIN COOK DROPPED ANCHOR. It must .have been on a Tuesday when Captain Cook dropped anchor outside Barrett’s reef at the entrance to Port Nicholson, as the records give the date as November 2, 1773. THE CALENDAR (“OLD STYLE AND NEW”). When it is December 25 (Christmas Day) in New Zealand it is December 12 in Russia, where the “ old style ” calendar of Julius Caesar is still in use, which provides for a leap year every four years without omitting the extra day three times in every 400 years. SCHOOL SUBSIDIES. One-third of the total number of pupils in the country, suburbs, and city must have been on the rolls in the primary schools in the rural districts, viz., 1300. A FINANCIAL INTEREST. The boys started with 19s, 16s, and 10s respectively, total 455. A’s 10 coins were 4 half-crowns, 4 florins, and 2 sixpenses; B’s, 2 half-crowns, 4 florins, 2 shillings, and 2 sixpences; and C’s coins were 2 florins, 4 shillings, and 4 sixpences. A lost 5s and B Is. A LEAKING SHIP. The steamer covered the 600 miles at the rate of 124 miles an hour, the vessel having taken 60 tons in 48 hours more than could be pumped out. ANSWERS TO CORRESPONDENTS. E. R. —There were over 200 received, and the greater proportion were correct, viz., 18 “ moves.” A condition was inadvertently omitted, however, otherwise the fewest would -be 20 moves. J. G. D.—As the responses were too numerous to mention even the initials of readers, a general acknowledgment was made.