Intellect Sharpeners.

New Zealand Herald, Volume LXIX, Issue 21100, 6 February 1932, Page 5 (Supplement)

Intellect Sharpeners.

MEASURE PROBLEM^ bit. l Barroa. v:? v A correspondent, " Rex," has sent * problem concerning of capacity, but as it is one with the three, five and eight quart vessels with which most readers and familiar, a poxjJe of tha same kind, hot with & five, seven and twelve quart measure, will he substituted. * A man had & twelve quart vessel foil of soar milk and was about to throw ft away when a woman came along for one (part of it, bringing with her a five-quart measure. Tfca man agreed to this, but did not see how one quart could be exactly. measured into the five-quart vessel, the only other measure he had being one of a seven-quart capacity. After-fifteen pourings the woman obtained of the milk in her five-quart measqjs. The question is what is the least nuniber "necessary with only these three vessels available, no tricks such as marking or tilting the vessels being allowed. A** pouring '* may be on the ground a$ well as from, one vessel to another. STAYS FOE FLAGSTAFF. On account of its elevation, 600 ft. above sea-level, twelva -aire siayji are required to secure in a vertical position the mast at a signalling station. The flagstaff is erected on a perfectly level piece of ground, five chains square, two or the wire stays that concern this problem being made of rigid steel, both fixed to the extreme top of the mast, and the pegs in the ground which held these two stays were in direct line with the point at which the mast entered the ground. The two - pegs in question are 42 yards distant from one another and one of the two stays is exactly 40 yards long, while the other is shorter than that by as many feet as there.;,j are yards between the tw<j "pegs. As ffejj|? r lengths of the stays are the exact distances from the pegs to the top of the pole, can the reader find the height of the mart and also the respective distances, from- pegs to the bottom of the flagstaff ? PUZZLE isi £ s. d. Here is a curiosity in pounds, shillings and pence which should test the inventive skill of the would-be solver, for the solution cannot be arrived at by any mathematical process known to" the writer, methodical trials being the most interesting form of procedure. A sum of money, less than £4O, in which pounds, and pence are represented, will, when multiplied by a digit not appearing in the sum referred to, give a result which can be expressed with digit® not heretofore used. That is to say, that in the whole operation ten digits, mchjag the cipher, are employed, none of which are represented. Can the reader construct such a sum and its answer! SHOPKEEPER'S SMAU. CHASGI. A shopkeeper whose, business requires him to have a good supply of small change en hand, keeps this ra a drawer containing seven one for each denomination of New Zealand currency, from £d to a hall-crown, seven in aIL On a recent occasion, before putting fresh change into the idfl, there was the same%nmber of corns m each of tES seven compartments, and the reader will be able to find from the folio-wing particulars what sum was then in each of the seven parts of the til?, as well as their number. ; Had there been one more coin-in each of two or the " silver " compartments the number of shillings represiaiied in the total sum would he in the prtgjorticn of nine to tssi to the total number of coins*, Without these extra two cams file amount of money in three of the compartments 5 could be exactly changed for seven halfj scveriegns, the sum in two of these re- } ceptacles being equal to that m the third. ] As one of these compartments held a sum i equal to 23a there should he no difficulty ! in answering the two questions asked. THE MAGIC SQUARE. " Gclenso " asks why it is that "15 '* Is the only number that fan occupy th® central cell in a twenty-five "magic square? The answer to this question is that the assertion ■is not correct, because any number from one to 25 can be used in the central space so that horizontally, perpendicularly and diagonally, as well as in other combinations, the numbers will add np " 65." There is an arrangement of the numbers in such a square with '* 1" in the centre which if repeated in nine similar squares adjoining, any 25 cells in a group selected at random from the 225 ceSs will form a magic square. Can the reader arrange the original square with ' 1 ** a§ the central i figure which has these rfnarartemftics T

LAST WHEE?3|SOLTrTIOSS, Digits in a Square.—s27, 654, SSL Prisß Money.—The salary of each officer was £250 p.a. Tethered Animal. —The hedge could be nibbled fcr a distance of 34- yardsHedge and, a Gate.—From the point where the hedge cats the east boundary of the square block to the gate is 25 yards. M Patience " Puzzle.—lf the squares ara numbered 1 to 64, commencing man the top left-hand corner and reading across, a route in sixteen moves is as fellows:— From 23 to 29 to 51, 64, 8, L, 57. 58, 20, 15, 55, 54. 22, 19, 59, 60, 28- TEs is the fewest number possible. ANSWERS TO COTERKSPOMDEaTS. —The process mentioned it inapplicable in the case yon refer to. " Curious." —According to aothorilia* on the it is a fact that an accurate model of a machine will work satisfactorily while the machine itself will not do so.

" Mathematics."—The qaesiion set by examiner is solvable from the data given. This answers "ELM.," "Cnrioras," "Teacher" and D.iL" Upon' receipt of addressed stamped envelope "working** will be forwarded.