INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVI, Issue 20217, 30 March 1929, Page 5 (Supplement)

INTELLECT SHARPENERS.

STATE LOANS.. .L 'r ■ ) B1 T. L. BRITON. Investors holding £10,000,000 of AuS* tralian three per cent, stock (issued when money was much cheaper than at present), decided to realise, and sold out at 94£ investing the money in four per cent. New Zealand stock at 105. As the former was more favourable to the issuing State than the latter, can the reader say by howmuch per annum the investors benefited by selling the Australian stock and purpurchasing New Zealand? " COUNTING- THEM OUT." Take 21 cards or counters numbered from one up, consecutively, and place them in the following order in a circle, viz.: 1, 14, 15, 17, 3, 7, 15, 6, 20, 2, 19, 21, 5, 18, 8, 11, 16, 9, 12, 4 and 10. Start at any number calling it one and count them one, two, three four, etc., in the direction that the hands of a ciock move, and when your count agrees with the number of the card it should be removed and tho count continued starting at the next card calling it one as at first until the whole have been " counted out.' : In the arrangement given above it is. not possible to " count out " the whole of them in 21 such counts, but by changing the position ve«y slightly'the feat can be accomplished. " To illustrate the method to be followed let us start at 20 calling it " one," then " five " would be the first card to be removed and another start maris at "IS " calling it one and so on. The puzzle is quite well worth trying. TWO ARMCHAIR POSERS. In a cricket match three batsmen. 'A, B, and C, only scored 90 runs -between them, A and B opening the inning 3 and C going in at first wicket down. Now if A scored half as many runs as the other two and A and G twice as many as B made himself, what were their individual scores ? In numbering the folios of a book of 100 pages, can the reader say without going through the tedious process of actually counting them, what is the total number of figures used ? For example, in a book of 20 pages the total would be 51. Both these questions are quite simple yet they may give the reader a few moments of thought, for he will, of course, not seek the help of - pen or pencil in answering them. CYCLING AND WALKING. Fully understanding a problem by 'eading carefully the statement of it is always an essential factor, helping one to 'a quick solution, and the following calculation is one in point. A cyclist travelling from X to Y walked half the distance and cycled the other half and returning by the same route he cycled half the time and walked the rest. Now, assuming that he maintained uniform rates of speed by the respective methods of travelling, both going and returning, can the reader say which journey occupied the longer time, and what is the distance between the two places if the outward trip took 7g hours, the walker travelling at an even rate of a furlong every one and a-half minutes ? The speed of the cycle was 880 ft. per minute. ONE HUNDRED OF EACH. There were exactly 100 boys in a school which comprised three divisions, namsly, A, B and C. Now, if 100 oranges be divided between the whole of the boys, giving those in A division three each, those in B two each, and those in C half an orange each, there could be many ways in which the numbers of pupils in the respective classes may bo made up to the full complement of 100. But let us limit the composition of the classes to a fixed number of boys in, each, by stating that those in A received ten less than half the number of oranges distributed in B class, and that the ones in C received altogether ten less than three times as many as the number given to A. How many boys were in the respective classes ? .

LAST WEEK'S SOLUTIONS. "*• en »■ V.: The Winners Lose. The seven players, T, U, V, \Y, X, Y and Z, started with 37s sd, 18s 9d, 9s sd, 4s 9d, 2s sd, Is 3d and Sd respectively. By Rail and Car. Under the conditions stated, the traveller's time would be worth 2s 6d per hour. The Length of the Trip, The distance was 250 miles. Tourists at Breakfast. There were ten in the party originally, eight of whom paid 10s each, instead of 8s if the other two had remained. A Curious Chain. There are 72,253,459 different ways fhat tho chain could ho reconstructed under the condition set out in the problem. ANSWERS TO CORRESPONDENTS. Bex.—Yes, coins were made in the reign of the first. George, but if the ore you mention is marked " George I." it obviously was not issued in that reign, and its genuineness would be open to question. " B. and H."—The correct answer to your inquiry is a gain i;n weight of 21b. " Half Acres".—A reply was sent in your addressed envelope as the matter was too technical to interest most readers. " A Reader". —The answer is as you have found, and it appeared on March 23. G.C.H.—The interesting item will be looked into.