NUTS TO CRACK.

Otago Witness, Issue 3801, 18 January 1927, Page 61

NUTS TO CRACK.

By

T. L. Briton.

(For th. Witness.) Readers with a little Ingenuity will find In iis column an abundant store' of entertainment and amusement, and the solving 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 sledge-hammer to crack them.Solutions will appear in our next issue together with some fresh “nuts." Readers -re requested not to send In their solutions, unless these are specially asked for, but to keep them for comparison with those published in the issue following the publication of the problems. SLEEPLESS NIGHTS. It has not been reported, as far as I am aware, that anyone has spent sleepless nights, or unduly wasted the ...idnight oil in trying to crack the “nuts” found in this column. It has, however, been stated that a certain schoolmaster in the country, stationed at X—, has -somewhat suffered in health owing to his super-strenuous efforts to discover the solution of t’ following little problem. Of course, if I were satisfied that this was a fact, it would undoubtedly cause some hesitation in publishing it, particularly as ihe endeavour is made in this column simply to carry out its purpose of providing the material for mental exhilaration only. But I somewhat doubt the rumour, so here’s the problem -. — Find a common divisor for the following three numbers that will leave the same remainder in each case: —2140, 3597, and 5550. THE FOUR ABSENTEES. A certain number of gentlemen went into a city hotel to dine during the holidays. Although they were obliged to sit at different tables, their spokesman told the head waiter to let them have the account in one bill The arrangement between the members of the party was that the amount should be equally divided between them. Just as the meal was over, and before the bill was presented, four of the party were called away. When paying the_ account, which was found to be exactly £5, the remaining gentlemen found th-t each had to pay 4s 2d more than thev , would have been called upon to pay if their four companions had not withdrawn before the bill was paid. How many were in the original party ’

NO CHANGE GIVEN. During the Christmas rush many of the toy shops were so crowded with customers that all hands had to be put on the serving counters. At one estaolisnment the cashiers were so overwhelmed that the management was compelled to announce that no change could be given, and it asked patrons to assist by tendering the exact amount. Two ladies waiting in the queue at the pay desk were discussing the awkwardness of the situation, when one said: “My account is less than ss. yet I have to give away five separate coins, as it can’t be paid in fewer.” ’ “ That. is curious,” said the other, “ ray account is more than ss, but less than 10s, yet the smallest number of coins it can be paid in is also five? “Let’s put the two accounts together,’ said the first, and save our small change by paying in one sum.” But when they totalled up the amount they found that it also necessitated five separate silver and copper coins to pay it without requiring change. What amounts? were the respective accounts? HALF AS DEEP AGAIN. Before sending in a tender for the building of a large terrace of threestoreyed houses, a contractor employed a man to put down a couple of shafts on the site in order to test the subsoil. . 1 was passing by that way after the man had started on the first —in fact, he had then dug down several feet, —and I asked him how deep was the hole. As he seemed rather pleased at the opportunity to talk, I ventured another question, chiefly with the idea of giving him a little respite from his toil, for the day was very hot. The second question was how deep would the hole be when finished. “ Well,” said the man, mopping his perspiring face, “ I am going down half as far again, and when finished, the top of my head will be as far below the surface as it is above it now.” Scenting a little problem, I asked “ What is your height?” He replied “ sft 10in.” I thanked him, and walked on. How deep would the hole be when finished? THE TWO TYPISTES. Quite a number of readers, some as far north as Whangarei, and many in the

South Island, have written for an explanation of the “Two Typistes” problem, as they could not follow the mathematics of the solution given. For the benefit of new raiders it may be stated that the point wnich does not seem to be clear to those cortespondents is as follows: Each typiste’s salary is £5O a year, payable half-yearly, with a yearly increment of £5 each. Miss Remington received her increase, halfyearly, whilst her colleague was paid hers annually. In the solution I stated when dealing with that phase of the problem, that in five years the former received exactly £l2 10s more than the latter, and that is the point at issue. Perhaps the letter of Mr L , of Box 1245, Wellington, which is typical of the rest, may be quoted from. He writes: “I generally get most of the problems solved correctly, but’ the 'two typistes’ beat me. Surely they must receive the same amount, irrespective of the pay days.” I will explain the matter more fully. At tho end of the first half year Miss R. received £25 plus £2 10s, or £27 10s. Her salary, therefore, during the second half-year was £27 10s, whereas her companion in that period was still receiving £25 only. Miss R. received her next increment of .£2 10s (£5 in all) at the end of the year. Where the other typist received her £5 in one sum', each receiving £3O. Miss Remington therefore received £2 10s more than the other in the first year,, end £l2 10s more in five years. Simple, is it not? SOLUTIONS OF LAST WEEK S PROBLEMS. THREE CITY CLOCKS. The three clocks haying started together to strike 12, made their second strokes two eeconds, one and a-half seconds, and one

second afterwards respectively, and as “Big Ben” took 22 seconds to strike 12, it follows that this clock struck its fourth time, the next clock its fifth, and the smallest its seventh together, exactly six seconds after commencing AT CRICKET. It is obvious that the number of runs that the batsman was entitled to score depended upon which actual runs were short. In the match in question I was able to tell the scorers that both batsmen ran the first and third short, and one the fourth. The scorers, therefore, properly recorded three runs to the batsman making the hit, notwithstand- ■ ing that one umpire called two and the other three short. It could, of course, result differently in cases where the umpires' had called similarly—e.g.. one batsman might run the first, second and third short and the other, the fourth and fifth, in which case one run only world be the correct score, AN ‘AVERAGI*’’ POSER. The average rate for the full iournev that a car makes, when it travels at 20 miles an hour going out, and 30 miles an hour returning by the same route, is 24 miles an hour, not 25. A little curious but still a fact. z ANOTHER CHARTTABLE SPORT. The gentleman distributed exactly £5. JOHN GILPI’S WILL.

The estate should have been divided in the year 1860 in conformity with the terms of the will,.

THE SOMEWHAT DIFFERENT CROSSWORD PUZZLE.

A large number of solutions were r&i ceived, but only about 14 per cent, of them were correct. These were from S.H.W., G.A.L., H.F.P., R.A.L. D.M.8., 1.M.W., A.E.K., H.D., D.E.R.. C.W.C., W.G.D., A.M., C.J., and G.B.D.