NUTS TO CRACK.

Otago Witness, Issue 3842, 1 November 1927, Page 32

NUTS TO CRACK.

By

T. L Briton.

(For the Otago Witness.) R.„dera with a little ingenuity will find in ils column an abundant •tore of entertainmer’ and amuseta«ni, 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 erack them. Solutions will appear In our next Issue together with some fresh "auts.’’ 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. Readers are requested not to send in their solutions, unless these are specially asked for, but to keep them for comparison with those published on the Saturday following the publication of the problems. THE NEW ZEALAND CRICKET TOUR.

The other day four Australian tourists to New Zealand were discussing our representative cricketers, and remarked upon the excellent all-round form they had shown during their tour at Home. They all agreed that their cricket deserved much larger gate receipts. One of the party | thereupon suggested sending a subscription I to the Cricket Council for the touring expenses fund, and after conversation this j was decided upon, the amount to be sent as a joint donation and to be equally subscribed. When counting their money, A found that he had exactly one-third more in his pocket than the required amount, B was £1 short, C had only one-half the sum that each agreed to .give, while D had twice the amount of a single donation. The whole of the money was therefore pooled, and D forwarded the sum agreed upon, their own personal accounts being adjusted afterwards. The total amount thus rooled was £l4 4s 6d, and it this was in excess of the joint donations by exactly one shilling more than the sum that one of the party put in what amount was contributed by the tourists? ONE TREE PLAIN. A manuka tree grew all alone on a small plain in the North Island. The land had been fenced many years ago, but most of the fencing had rotted away, and as it was intended to use the land for cropping it was decided to erect a wirenetting fence on + he old boundaries, the lengths of which were 8 chains, 4.5 chains, 10 chains, and 6.3 chains respectively. As the reader knows, the area of a figure of this character with stated dimensions will vary according to the shape it assumes, but if it be granted that the manuka tree was exactly the same distance from each of the corner posts, can the reader calculate the area of this paddock? This is a practical problem which is ridiculously simple of solution, provided the solver goes the proper way about it. Otherwise a lot of unnecessary figuring will be involved. MALT VINEGAR. Three casks contained malt vinegar of equal strength, but of different quantities. For a special purpose it was necessary to transfer a portion of the contents of one cask to another, and it was done jn this way:—One-third of the vinegar in No. 1 barrel was drawn, and two-thirds of it was transferred to No. 2 cask, the remaining portion of that withdrawn being placed in No. 3 barrel. One-sixth of the contents of No. 2 was then poured into the latter cask, which at the same time received one gallon more from the No. 1 barrel. There were 105 gallons altogether, none of which was spilt during the operations. and as each cask held the same quantity when the transferring was completed what quantity was in the respective casks at first? IN THE CASH BOX. A European lady who suffered by tha failure of privately-owned banks in the ■’ Far East,” now keeps her own current account, and pays all her bills in cash. To enable her to do this she arranges with on e of the foreign agencies to draw her requirements in cash monthly, and she keeps the money in her own cashbox in English currency only. She had an account of £7 3s 6d to pay on one occasion and tendered it in sovereigns and halfcrowns, giving the change that was over to a local charity. 'The next day another bill was presented to the amount of £3 Is fed, which was (raid in the same value coins, as these were the only kind in the cashbox. In the latter payment double the number .~.f sovereigns was tendered as in the first account, and half the number of halfcrowns that were handed out when paying the bill of £7 3s fed. If in paying both accounts one-half the number- of sovereigns and one-third the number of halfcrowns ' that the cashbox held, were given away, what sum did it hold at first? “IN AMERICA.” The boys in the Sixth Standard of a < crtain school have been much exercised over a question put to them by the headmaster, who has promised a half-holiday to the first boy giving the correst answer. Here is the question: There is a village situated in an exceedingly deep valley in a certain part of the world, where the sun at midday is nearer to its inhabitants by 3000 or more miles than it is either at sunrise or sunset. Where is the “valley situated? The lad who brought the question to me for solution thinks “ it must be in America.” I told him that it would be a nity vo spoil such an excellent incentive for the boys to search their geographies and atlases by giving a reply then, but it will be published in the Daily Times on “Guy Fawkes Lay,” which will be the Saturday following this issue. In the meantime can the reader find where this wonderful valley is situated? The writer has seen a deep valley to which these facts apply. LAST WEEK’S SOLUTIONS. EQUIDISTANT. The distance that the gentleman would have to travel from any of the three stations X. Y. or Z, to his house was 1980 yards (one mile one furlong).

AT A WINTER SHOW. As the money spent by each of the eight boys must have been an exact number of shillings, no smaller change was held by anyone. A’s younger brother must nave been G. the two together spending 6s. The total sum spent was 325, each of the boys receiving Is out of the balance. a. CRICKET BALL. TENNIS BALL. AND FOOTBALL. (1) The volume of the football (a spherical one) was 523.6 units. (2) The diameter of the sphere must have been six inches under the conditions stated, and therefore a smaller sized one than that referred 'o in No. 1 solution above. PROBABILITIES.

(1) There are 32 different ways in which the coins can fall. Out of this number there are only five ways that thej’ can fall with four heads and one tail uppermost. The probabilities, therefore, that this will happen in one attempt are five to 27, which means that there are only five chances out of 32 in favour. (2) Five shillings and ninepence is the correct amount, one-fourth of a sovereign plus three-fourths of a shilling equalling the amount stated. COLD STORAGE. 1728 boxes could be packed in the chamber, as each measured 12 inches by 10 inches by 8 inches. But the one-inch battens under the boxes reduced the number of tiers to 11. so the maximum number would be 144 fewer—viz., 1584, the capacity of the chamber being diminished by 80 cubic feet owing to the battens.

ANSWERS TO CORRESPONDENTS. “Waipahi.”—The multiplier must be regarded as an abstract number. Therefore two shillings cannot be multiplied by two shillings. But don’t ask why two inches can be multiplied by two inches, because it might raise the old perennial concerning “ square money.” “ Mac Sf ar,” Balclutha.—There is no definite information, but there must be considerably over 900 distinct languages. There are several hundreds in Africa aloue, and in the New Guinea zone of a thousand miles around, British Papua, the British and Foreign .Bible Society considers there are not fewer than 83 distinct languages, and not*merely dialects, just as in Great Britain we have

five—viz., English. Welsh, Gaelic, Erse, ami Manx. The Bible Society has alone published the Bible in 595 languages, and there are about 200 by other agencies, the society’s record being, it is stated, less than seven-tenths of the total.