INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVI, Issue 20229, 13 April 1929, Page 5 (Supplement)

INTELLECT SHARPENERS.

Br T. L. BRITON.

A HERMIT'S MONEY.

Most people no doubt havo read of the eccentric distribution of his money by the hermit Marin, long before Brewster gave his miliums away, and will recollect how mathematicians were at variance over the exact amounts to be awarded the beneficiaries.' The strange fancies, which led the Frenchman to disgorge his wealth in the last few days of his life in order "to make others," ho said, " as unhappy as himself," prompt this, problem based upon his superstitious belief that the number seven pos sessed sinister influences. " Let us suppose that Marin distributed one million francs among a certain number of persons not giving to anyone more than one amount, the sums being exactly either one franc or some power of seven, lor example seven, 49,343, and so on. 'l'he problem is how were the million francs divided, and- how many people shared if not more than six persons received the same amount. There is only one answer to this question, and it may bo arrived at by trials, though there is a direct and easy method by using the septenary scale, a system perfected by that clever mathematician, IT. E. Dudeney. The reader will probably' be surprised to find "few people could benefit under these conditions. WHAT TIME WAS IT? After studying his watch for a moment or two, Hopkins upon being asked the Lime replied as follows:—"If one quartei of the timo that has passed since noon to-day to the present moment be added to exactly one half of the time that must elapse between now and noon to-morrow, the result will be the precise time it is by iny watch at this instant."' In calculating what time it was when Hopkins looked at his watch the reader should use tho method of measuring time by dividing the twentyfour hours into a.m., and p.m., and not adopt the system by which the time for instance could be half-past fifteen. SERVIAN WAR FIGURES. During the Great War there were many records of battalions and divisions being almost annihilated. Reading the other day of the Serbs and Austrians in their conflict in 1916, some of the numbers given suggest an interesting problem for by interchanging some of the figures, a curious coincidence is 'tevealed. There were three Servian regiments, which lost very heavily in an engagement in the spring of that year, and to find the largest number, who were killed in any one of them A B G, and with only the following details available, should give the reader something to sharpen his. intellect. After the conflicts the difference in the number of men left in A • and the number left in B was the same as the difference between the numbers left in li and G Now can the reader lind the smallest number of men left — or the largest number killed —in any one regiment as mentioned above, the only additional information being that the numbers —all different—of the men left in any two of them added together firm a square number. Each regiment went into action with 10,000 men, and the question is what is the smallest number of men that could be left in any one of tliem ? LIMERICK AND AUSSIE. Although it is a matter of record that one of tnese champions beat the o:her recently on level terms let us assume for the purposes of a problem, that the next mile race resulted in a dead heat. Aussie led Limerick by half a length at the end of the first two furlongs, and by a length at tho half-mile the three-quarter mark being passed bv the two horses locked together in one minute seven and a half seconds, running in that way to the judge's box, the verdict being a dead heat. Now if Aussie ran at a uniform pace throughout the race, running each of the first two furlong laps in half a second faster time than his adversary, how fast did travel the distance between the half mile and six furlong posts? This simple calculation does not require the use cf pen or pencil. TWO ASSESSMENTS. An Aucklander was discussing witli a resident of X the merits of_ the two controversial systems of municipal assessments. Upon comparing notes it was found that the amounts of their own assessments were exactly the stme, though A pays £9 3s 4 more in rates than his friend B. Now if A's city has a rate of 2s in the pound while that of the other is only Is 4d can the reader say without requiring tho use of pen or pencil what is the exact amount of tho two assessments, for like the previous problem lfc is ono for mental calculation cnly. LAST WEEK'S SOLUTIONS. An Unprofitable Consignment. The original cost of the corrugated iron was £4l 13s 4. Three Instead of Seven. X started with 13s, \ with is and Z with 4s, the former thus losing 5s as each had 8s at the finish. A Railway Curve. The radius of tho curve must be 2 miles 10 chains, being on the map as stated. On Holiday Bent. Bill spent £2 0s 6d exclusive of railway fares, which were 6s each, tho former amount being 9s more than the average for the seven men viz: £l lis 6d. Two Granite Blocks. The height of the large one was 1 l-7ft. and the other 3-7 of a foot, the cubic measurements of the two together being tho same as the lineal feet of both viz: 1 4-7. ANSWERS TO CORRESPONDENT. r " 1 " D.S.—Your diagram shows a correct solution. " Three Lines."—lt is only solvable by trick, otherwise the position is practically impossible. C.H.D.—You are quite, right as there is no general law governing the large number of correct answers. " Judco "—(1) Given with the aid of instantaneous photography it » difflej" 0 seo how it would bo possible to the distance mathematically. latively. •« Te Miro."—Thanks. Will await receipt of diagram referred to. " Wheel."—Neither point moves at a uniform speed throughout. " Cricket."—ln the case mentioned it is obvious that the four innings wem IBU, 148, 124 and 106 runs respectively. C.T.L- No matter where the two objects are placed in relation to the point, the conditions already stated will always obtain*