INTELLECT SHARPENERS.

New Zealand Herald, Volume LXV, Issue 19838, 7 January 1928, Page 5 (Supplement)

INTELLECT SHARPENERS.

* >Z ft L BBJTO*,, Headers ara requested not to sand in their solutions unless these are specially asked for, but to keep them for comparison with those published 021 the Saturday following the publication of the problems. DARKNESS AND GANDLEB.

The requisition for the despised caudles in the House of Commons during the breakdown of the electricity Bervice recently supplies a little problem. Let it be assumed that the candles placed on Mr. Speaker's bench, as well as on the tables of Ministers, were of the largest size, viz., diameter, and guaranteed to burn for 9 hours each. There being not enough of these to go round, members were supplied with tapers of the ordinary kind, lin. in diameter, which would only burn for 6 hours under similar conditions to tits larger ones. Assuming all candles were lit simultaneously, burnc-d uniformly according to the duration stated, and extinguished when the electric light was restored, how long was the installed illumination out of action if the Speaker's and Ministers' candlos allowed each remaining length to be one and one-fifth times that in each of the smaller ones ? The candles originally were,-of course, all of uniform length, and were lit immediately the electric light failed*

A MAORI WAR MEMORY. A garrison stationed near Kihikihi rt the time of the Waikato war was provisioned for as many days as wera equal to the number of Jtnen who comprised it. After 130 days, a reinforcement of 374 extra man arrived, being all that were left of 450 who had left Auckland two' months previously, and were ambushed on the march. As no extra food had arrived, the whole garrison was thereupon placed on half-rations. If, by thus reducing the fare, the provisions were made to last 280 days longer than the time it was provisioned «£or, what was the strength of tho garrison before the arrival of the reinforcement, in view of tho fact that there had been no losses ? SMUGGLING AND POACHING. A party of smugglers, being forewarned of tne approach of, coast-guardu, planted some gold in an obscure place, but when they returned some nights afterward, found it had been stolon. Three poachers who were in concealment had witnessed the burying of the treasure, and next night removed it as follows:—£4000 to Hickey, £2500 to Kennedy, and £ISOO to Whalley, total, £BOOO, all in sovereigns, each man securing his share in his own sack. They decided to cross the river at a lonely spot where they had left their small boat, but although it would just hold two men, it could only carry one with one sack. These poachers had no confidence in one another, 30 no one was left alone on shore or in the boat with more than his portion of the loot, neither could two together be trusted with more than their joint shares. How did they all get over in the boat without assistance of currents, ropes, or similar device, with tho gold also inside the boat, and what would be the fewest crossings necessary? AN AWKWARD DIVISION." Three cyclists, who were late in arriving to meet their mates at a woolshed, found that the shearers had " cut out," and gone to town, leaving a note directing them to a small keg containing six quarts of ale. The cyclists decided to divide the beverage equally. For this purpose they found three suitable petrol tins, but could only .find a five-pint measure and a three pint jug to apportion the quantities desired. They managed to accomplish the required division, but from what one of them told the local schoolmaster afterwards, they must have' made nearly twice as many operations as were necessary. What are Hhe fewest number in which an equal division can be effected by using the two measures only, if each " pouring" from one vessel to another constitutes ah operation?

A SQUARE HOUSE. A question put to the company at Jin evening party recently aroused much interest and kept everyone engaged until the time arrived io prepare for home. It was v this. Would it be possible for a square house to be so designed, that when built, all the windows on the four sides —• all flush with the walls—would have a northerly aspect T There were two architects anfi also an expert mathematician present, and if the correct answer had occurred to them, they kept the secret, for up to parting the " nut" had not been cracked. What is the solution? LAST WEEK'S SOLUTIONS. Coins and Squares. The largest possible amount that can bo shown, is 255. The pitfall of which tlio reader was warned, is that a solver would very naturally endeavour to place the highest value coins in as many squares as are available under the conditions. If this were done, however, two • sqiiares would have to remain vacant, and so three squares and not four (as bo possible), should be occupied by 2s coins, the 2s 6d ones only being placed m four squares to show a total of *?ss. Nsar the Assuan Dam. The diameter of the irrigation a.ca was 40 miles. The Arab walked 6§ miles, and the Bedouin 5 miles in an hour :vnd forty minutes, while the chain-man walked 25 miles in 5 hours, the respective rates being 4, 3, and 5 miles an hour. A Field of Oats. The area of the oblong field was 19 * acres 32 perches, the sides being 12 and 16 chains. The 44 yards wide strip (2 chains) all round the field embraced 85 square chains, or 9 3-5 acres. The Same Block of Land. The width of the striip reaped round the field was just half that of tha previous problem, viz., one chain, the-total area of the strip being 51-5 acres. At An Eating-House. The country visitors must have stopped five days, during which 9Q meals wera served. There are; 15 different ways that the friends could be seated two at one table. ANSWERS TO CORRESPONDENTS. D.C.H.—The problem said " uniformly." T.T.—-They are called " eccentric" wheels. T.C.A.—The " working" will ™ on receipt of addressed stamped envelope. R.P.—The hurdles could that the area would net ne larg for one s h es P*^—