INTELLECT SHARPENERS.

New Zealand Herald, Volume LXV, Issue 20058, 22 September 1928, Page 5 (Supplement)

INTELLECT SHARPENERS.

THE WAHINE AND MAORI. BY T. L. BBJTON. Between these two excellent packets it will be assumed for problem purpose* tl'iat under equal conditions there is no chtierenee in their rales or steaming, and tiiafc the trip between the ports of Lytieiton • and Wellington is usually covered by them in about the same time. During the heavy gales in August this regmaiity was somewhat upset, and it is with one particular trip when the Maori was making the run to Lytteltou in the teeih of an abnormally heavy blow from the south, that' this problem is concerned. Let it bo 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, tho Wahine, leaving the southern port at tha 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-eights of the full distance between the two places, and as both steamers continued at these" relative speeds uniformly throughout, the Wahino taking exactly ten hours for the trip, how j much was the Maori longer than tha turbine vessel in arriving at her destination? DIKING TOGETHER. Afc 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 hi 3 wife. If at tho next meal it was desired to change tha relative positions of the diners, maintaining, however, the conditions mentioned, it 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, and the little problem for the reader to solve is in how many different ways can five married couples be seated at a round table so that each will have a lady on • either side of him. but not his wife ? Tha smaller number of 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 tha number of married couples were larger. It is, however, solvable mathematically under any conditions. A HABERDASEEEY SHOP. A haberdashery shop keeper when making up her Saturday's account sales, found that the following classes of goods were sold that day:—Buttons, pins, needles, tape, cotton, calico, ribbon and silk. None of the goods were priced the same, yet, strange to say the total amount received for each kind was identical, the day's takings amounting to £1 15s. Tha buttons were sold separately, the pins and needles by packet, the cotton by reel, the tape by the knot, and tho three other articles by the yard, and if only one of each kind had been sold tho total receipts would have been Bs. It. will give the reader an excellent opportunity of testing his ingenuity, by asking him to find how the bill for £1 15s is made up. There were IS2 units sold, tha price of each being an amount that can be paid in New Zealand current coinage. THE SOUTHERN CROSS, According to reports the stay of the monoplane Southern Cross at Suva was longer than intended according to th« aviators' intinerary, and when they left very few people knew of it. The NewZealand agent here 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 the information in the following cryptic form. "If tlie day sifter trie day befdrfst ,::> ; tho day 'following the clay that they ' hopped oft* ' 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, tho number of days intervening between tha ' hopping off '"day and the following Saturday, are 'exactly as many as the number of days between the day before tho day before yesterday and the day thai the aviators ' hopped off '_ on their last lap to Brisbane." In asking the reader to say what day of the week that was, ho may perhaps be that Suva, unlike Samoa, being west of the _ 180 th moridian, has its days of the week identi- , cal with New Zealand. A NOVEL FAMILY RECORD. Jones planted a tree on the day ha was married and one every anniversary afterwards, the row' running north from the first one. At the request of his wifo he planted one on the south side of tho 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 f lad being now a schoolboy, and to-day" there is a fifta 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. Tho 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 tho total ages of the 21 trees are 381 years, how old was the original tree when the youngest son. was born ? LAST WEEK'S SOLUTIONS. Choice Cigars. A received three full boxes of one half-full, and three empties; totals, seven boxes, 175 cigars. B received two full boxes, three half-full and two empties; totals, seven boxes, 175 C received two full boxes, three half-full, and two empties; totals, seven 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 " Manclros." If the seven squares , he numbered ono to seven the three " Mings being on two, three and four, and the " Manehus on five, six and seven, the following ten moves will place the latter on one, nnd three, and the " Mings on four, five and six, leaving number seven blank. Ten moves are the fewest possible. The Same Photograph, But! The man who, upon looking at tho photograph, stated that the one in tho , picture had no brothers or sisters, must have been a grandson of the person who, upon looking" at the same photograph, said: "That" man's father is my father's son." Harriers. The harrier who started last caught tho other at a point exactly 26 miles . from the rendezvous at the 150-mile post, just 2 2-3 days after the scratch man started. A Debated Point. Hopkins must have lost even tho'-~h he won as many, games as his opporrrt, and tho stakes revel, the order in whi.-h he won his six games being immaterial At the end of two games be must Iwe lost a quarter of what he had if lie won one of them; in four games he would Hso seven-sixteenths of what he commenced with and so on. It's a curious position and to most people nothing but a practical demonstration is satisfactory. ANSWERS TO CORRESPONDENTS. " Limelight."—-Your query wrongly, ad- - dressed. In any case the official rc:e«-v Honed is not now an " M.IV though these two letters happen to stano " much photographed " as suggesi«a* I