INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVII, Issue 20508, 8 March 1930, Page 5 (Supplement)

INTELLECT SHARPENERS.

BUYING A SECTION.;

BT T. L. BBIXON.

An unoccupied section of land onequarter of an acre, adjoined a section belonging to a man who desired to increase his own frontage by 15ft. But a3 the section, under the terms of a will,.,could not be subdivided, the man purchasedthe whole of it, and after excising tho required 15ft., sold the balance of tho quarter-acre block. Assuming that the price he paid for the section was £I2OO, and that after fencing off the portion of the size mentioned, he sold the remainder of it for £IOBO, which meant that ho had secured the desired strip 15ft. wide, at the rate of £8 a foot, how much per foot did the purchaser of the balance of tho section pay, if tho price was £2 a foot more than it cost tho first-named man ? PAIR AND HEAD WINDS. Although the question is old, and one that has been debated by many generations when applied to the tidal influence upon the progress of a steamer, the point can always be depended upon to raise a controversy. A correspondent " Air: Pocket" has brought tho matter up concerning the influence of the wind upon the flight of aeroplanes, which mathematically is tho same thing. Here is his query" Would you please decide the question as to tho relative times taken by an aeroplane under the following conditions. On a nonstop flight from A. to B. it encounters a head wind blowing in an exactly opposite direction at a velocity of ten miles an hour, and returned under exactly similar conditions as to engine, route, etc., with tho same wind still in force.- Would the machine take a longer or shorter time to make the return trip in dead calm, if the number of engine revolutions and all ether factors were the same as in tho flight' mentioned?" Perhaps some readers who have not given consideration to the point raised, wouldi like to think over it. Tliq reply will bo published next Saturday. SCORE-ANH-ONE FAIR MAIDS. Twenty-ono fair maids—"grown-ups'' down to little " tots " —sat in a row to hear ono of the travelled Girl Guides relating her experiencQS, and strange to say that, although most of the older ones ail looked the same age, one of them, the eleventh counting from either end, admitted that she was older than any of tho others. On her left-hand side the onn beside her was two years younger, and right down to her end, each succeeding girl was two years younger than her neighbour on the right. The same regu- . larity existed in the row on the eldest maid's right-hand side, but the ages between them was uniformly one year only, that is, commencing with the eldest's right hand neighbour-—who was a year younger —right down to the end on that side, eat-h succeeding girl was a year older than her right-hand neighbour. If the youngest of the whole party of 21 is exactly one-third the age of the eighth youngest, there being two maids of the latter age in tho group, can the reader say what their respective ages are, the total years of the 21 being 381 ? Excluding the eldest, onehalf of the group are twins. TWO POE THE PRICE OP ONE. A firm recently advertised suggesting to the family man who might be contemplating the purchase of a motor-car, that practical economy would result if he purchased two machines of a certain make, which could be secured at the price of one of a larger size, so that the man's wife and daughter could have one for themselves, thus reducing the total cost of upkeep as compared with the running costs of a large family ear. The advertisement -prompts a problem which the reader will doubtless solve before passing on ta the next, and of course, without the aid of pen or pencil. Let it be assumed that a still larger car was equivalent to three of the smaller machine!!, and that the price of each of the latter was £225, when sold to different persons, but if three were purchased by the same individual, they could be obtained for the price of a: larger one of a family size, £6OO. The question suggested by these conditions is what, is the cost price to the firm of one of the smaller machines, if the total profit on the" sale of three to the same buyer at the price quoted, was exactly the same as the profit made upon one. of them sold singly at the sale price mentioned ? CHRISTMAS AT AN ORPHANAGE. Here is a question involving the simplest of calculations, yet possibly it may not be correctly answered right off by every one who makes the attempt. _ During Christmas festivities at a certain orphanage, one of the many good things provided were bags of succulent sweetmeats. There were fewer than threQ hundred bag 3, and distributions were made four times during the day, one-quarter of the number on hand being equally allotted to the orphans on each occasion. There was a curious coincidence at' these four divisions, and that .was that each and every time the number of bags on hand were divided into four parts for the purpose of distributing one-quarter of them, there was one bag over, which on every . occasion was given to the custodian's little boy. So the reader is asked to find how many bags there were altogether, and how many orphans shared in the foui'th distribution, if each received then, two bags? It will be readily seen of course that the four distributions did not exhaust the number of bags, there being seventy-eight remaining at the end. LAST WEEK'S SOLUTIONS. •. ' • . •'•••■ | 'V ; At A Church Bazaar. Jones one hundred shillings and Smith ninety-nine sixpences and one threepenny piece, total £7 9s 9d. Leingth of a Wall. The wall when finished would be 27ft. in length, being 9ft. long when the conversation took; place the mason then stating he still had to go " twice as far." Simple Per Gentage Problem. The original capital was £BOOO. Catching a Train. Thirty miles an hour, the taxi cab start' ing off at four minutes to twelve to travel two miles. An Endless Chain. There are two methods of mending the chain that would be cheaper than buying a new one for 6s 6d., the cheaper being by breaking up the two pieces containing three and four links respectively, which when joined to the other seven pieces would cost 5s 3d. ANSWERS TO CORRESPONDENTS. rj g. The smallest number that fulfil all the conditions of your question is 158, eleven times sixteen less lo the number superannuated. Mutuus Consensus.—Thanks; it ssemed obvious on your first statement. Pakeha.—(l). " Wapiti" is the Indian word for tho North American elk. ,(2), The accent is on tho first syllable. ;