NUTS TO CRACK.

Otago Witness, Issue 3889, 25 September 1928, Page 69

NUTS TO CRACK.

By

T. L Briton.

(Foe the Otago Witness.) • Readers with a little ingenuity will find iu this column an abundant store of entertainment and amusement, and the solving ot the problems should provide excellent mental exhilaration. .While some o£ 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 are 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 ot the problems.

THE WAHINE AND THE MAORI. It will be assumed for problem purposes that under equal conditions, there is no difference in the rates of steaming of these two excellent packets, and that the trip between the ports of Lyttelton and Wellington is usually covered by them in about the same time During the heavy gales in August this regularity was somewhat upset, and it is with one particular trip, whe i the Maori was making the run to Lyttelton in the teeth of an abnormally heavy blow from the south, that this problem is concerned. Let it be assumed that under normal conditions the two steamers when leaving their respective ports at the same time pass each other midway between the two places. On this tempestuous trip, however, the Wahine, leaving the southern port at the same time as the other left Wellington, was abreast of her smaller sister ship at a point distant from the northern port equal to three-eighths of the full distance between the two places. As both steamers continued at these relative speeds uniformly throughout, the Wahine taking exactly io hours for the trip, how much was the Maori longer than the Wahine in arriving at her destination?

DINING TOGETHER. At a round table dinner laid for six, three ladies took certain places, and when their respective husbands were seated each found himself between two ladies, neither of whom was his wife. If at the next meal it was desired to change the relative positions of the diners and yet to maintain the same conditions, this, would not be possible, as there is only one such arrangement. With four married couples there would be only two different ways of thus seating the eight persons. The little problem for the reader to solve is in how many different ways five married couples can be seated at a round table so that each gentleman will have a lady on either side of him that is not his wife. The small number o five is chosen so that the reader can solve the problem by methodical trials if he so choose, though this plan would not be possible if the number of married couples were larger. It is, however, solvable mathematically under any conditions.

A HABERDASHERY SHOP. A haberdashery shopkeeper when making up her usual Saturday’s account sales found that the following classes of goods were sold during the day: Buttons, pins, needles, tape, cotton, calico, ribbon, and silk. None of the goods was priced the same, yet, strange to say, the total amount received for each kind was identical, the day’s takings amounting to £1 15s. The buttons were sold separately, the pins and needles by packet, the cotton per reel, the tape by knot, and the three other articles at per yard, and if only one of each kind had been sold the total receipts would have been Bs. The reader will have an excellent opportunity of testing his ingenuity in the attempt to find how the bill for the amount of £1 15s is made up.In order that there may be no confusion as to prices and quantities, there were 192 units sold, the price of each being an amount that can be paid in New Zealand current coinage?

THE AIRPLANE SOUTHERN CROSS. According to reports the stay at Suva was longer than was intended according to the aviators’ itinerary, and when they left very few people knew of it. The New Zealand agent, who had private information of their movements, was asked one day, while the airplane was in Fiji, on what day of the week they intended “ hopping off.” It appears that he knew that the aviators had departed that same day, but thought it a good joke to give them information in the following cryptic form. “ If the day after the day before the day following the day that they ‘ hopped off ’ were yesterday, the week would not be as far advanced as it was, but taking the days of the week at Suva exactly as they are in New Zealand, the number of days intervening between the ‘ hoping off ’ day and the following Saturday are exactly as many as the number of days between the day before the day before yesterday and the day that the aviators ‘hopped off ’ on their last lap to Brisbane.” When the reader is asked to say what day of the week that was, he may perhaps be reminded that Suva, unlike Samoa, being west of the 180th meridian, has its days of the week identical with New Zealand. A NOVEL FAMILY RECORD. Jones planted a tree on the day he was married, and one eveiy anniversary afterwards, the row running north from

the first one. At the request of his wife he planted one on the south side of the original .tree upon the birth of their first child, and one in the same row running south at the birth of each subsequent child. It is some years since they were married, the youngest lad being now a schoolboy, jmd to-day th«re is a fine row of ten trees on the south side and, of course, a larger number on the north side of the one first planted. This record suggests an easy problem, particularly as the ten children were born at intervals of exactly two years, the first one arriving two years after the wedding day. The planting was carried out strictly as stated, but the problem will be limited to 21 trees, 10 on each . side of the original, and it should give the reader an insight into a useful calculation. If the '.otal ages of the twenty-one trees are 381 years, how old was the original tree when the youngest son was born?

LAST WEEK’S SOLUTIONS. CHOICE CIGARS. A received 3 full boxes of cigars, 1 half full, and 3 empties; totals, 7 boxes, 175 cigars. B received 2 full boxes of cigars, 3 half full, and 2 empties; totals, 7 boxes, 175 cigars. C received 2 full boxes of cigars, 3 half full, and 2 empties; totals, 7 boxes, 175 cigars. This is the only way that an equal division could be made with the stated condition that no one should receive more than three boxes of similar contents. “ MINGS ” AND “ MANCHUS.” If the seven squares be numbered 1 to 7 the three “ Mings ” being mi 2,3, 4, and the “ Manchus ” on 5,6, 7, the following ten moves will place the latter on 1,2, 3, and the “ Mings ” on 4,5, 6, leaving No. 7 blank. Ten moves are the fewest possible. THE SAME PHOTOGRAPH, BUT! The gentleman wii-,, upon looking at* the photograph, stated that the one in the picture had no brothers or sisters, must have been a grandson of the person who, uprih looking at the same photograph, said, “ That man’s father is my father’s son.” HARRIERS. The harrier who started last caught the other at a point exactly 26 miles from the rendezvous at the 150 milepost just 2 2-3 days after the scratch man started.

A DEBATED POINT. Hopkins must have lost even though he won as many games as his opponent and the stakes level, the order in which he won his six games being immaterial. At the end of two games he must have lost a quarter of what he had if he won one of them; in four games he would have lost seven-sixteenths of what he commenced with, and so on. It is a curious position, and to most people nothing but a practical demonstration is satisfactory. ANSWER, TO CORRESPONDENT. “ Limelight.”—Your query wrongly addressed. In any case the high official in London mentioned is not an “ M.P.,” though those two letters happen to stand for “ much photographed ” as suggested.