INTELLECT SHARPENERS.

Otago Daily Times, Issue 20644, 16 February 1929, Page 22

INTELLECT SHARPENERS.

By T. L. Briton. ANOTHER CRICKET POSER. A perusal of th e record of the Australian batsman Ponsford—in which his hatting figures in all test matches played both in England and Australia up to and including the first one of the 1928-29 season were given—suggested an interesting ami useful little problem. It will be remembered that Ponsford mot with an unfortunate accident in the first innings or the second test match, which debarred huni from playing again during tire season. Mis batting average was 40 runs per innings up to the end of the first test of the 1929 series. Although he was not able to get going '’ i u the match in which he was injured, lot us assume that he scored 96 in the first innings, bringing rVrn a 'lc rase j- up t 0 48 runs P er innings. y ’ UI few particulars can the reader determine how many completed innings he llacl , 2U’ to and inclusive of the first test oi 1928-29, Ponsford no*!: having secured a not out ” in any of the matches played. THE BLIND ABBOT. The following very ingenious problem has Lreen sent by “Puzzled” and the reader will find in it something that will give him quite a lot to think about. A blind Abbot was at the head of a monastery of 24 monks. The sleeping apartments were in a square building on tne first floor, which was divided into nine square dormitories of equal size, and the Abbot occupied tire central one, three monks being domiciled in each of the remaining emlrt, there being thus three compartments on each of the four sides of the building. To assure himself that all were duly housed each night, the Abbot regularly visited the dormitories, reckoning that if Ae found nine monks in each of the four rows of three bedrooms e\eiyt!nng was in order. One night, howinn’ n UF a,' nonks absented themselves. t>till the Abbot correctly found nine in tw lO i W °j t j* r ? e rooms. Next night inf os etUr ? e i bri "P> n g four others, makmg „8, yet the Abbot, when visiting at nnnl, nffi, again correctly found nine in * he rows, hour more were housed the and i an actional four rof n f eht a f erwa rds, yet th e Abbot’s correct count was the same as before ?W t lStaml fr K tha , t 0n ‘he latter visit there ere 36 monks in the emht dormitories. How could this happen? FROM PORITON TO QUAMBONE. to'o^afh started to walk from Poriton nvwi i b i? e ’ leavln S the former place at exactly half-past 9 in the morning. Walk- '” ° f a uniform speed without stopping, and a ' half af ter he started off ™® t , ll a f other ■l nan > Beaz|ey, who was a ‘ s ? tvalkmg uniformly at 2iis own rate d?d nnf h t° U i , aD ? del ‘Y' The walkers Afinnf but mer ?l y exchanged saluthnV & i remarkln g as they passed that he left Quamboue at exactly 10 o clock, half an hour after Atnery’e departure from Poriton. Each man kept up an even speed throughout without vanation, and Amery arrived at Quambone nair an wiour after noon\ precisely, Without concerning himself as to the distance between the two places. - or the relative rates of walking of the two men. can the reader determine the exact time that Beazley arrived at Poriton?

A RAILWAY MISHAP. Like other countries possessing railroads, J»ew Zealand is not immune from accidents in this form of transport, and a recent slight misihap to the engine attacbed to a passenger train on the Main .trunk line lends itself to the propounding of a little problem. The average speed of the train for a certain number of hours after departure was 30 miles per hour, when, owing to an accident to engine (which, however, caused no stoppage), only 12 miles were covered in tihe two hours immediately following the mishap, mu'? this reduced the average for the distance travelled to 26 miles per hour. The point that the reader is asked to dear up from these ln i e ? f s. re ., tal k. is number of hours for which the train had been travelling betore meetir- with the engine mishap. A young student friend to whom this question was recently put stated that the data given would not enable the problem to be solved, but no doubt the reader will be able to arrive quickly at the correct solution without further information. POSTAGE STAMPS IN CHANGE. During a holiday stay in the country recently I had occasion to make a few small purchases from a city shop, and enclosed £1 to cover the cost of the articles, etc. At the same time the shopkeeper was asked to forward the change in postage stamps—an equal quantity of penny and halfpenny stamps if possible. It so happened that the amount due in change could be apportioned in this way, but the clerk misread the instructions, sending penny stamps for half the amount and halfpenny stamps for the balance. Here then is a little problem on the point. If the total number of stamps thus received u eigii t more than would be correct had my request been acted upon, can the reader determine what was the actual sum due in change? He will find that the process of making the calculation will give him a moment or two of refreshing mental exercise, particularly if the use of pencil and paper is eschewed in the effort.

PREVIOUS WEEK’S SOLUTIONS. THE PARTY OP ONE. There is another way in which the relationships mentioned can be correctly claimed by one person, but the example given is the simpler and more likely to occur. BY CAR AND MOTOR CYCLE. The man must have travelled threequarters of the whole distance on his motor cycle, viz., 45 miles. THREE MEN RAN IN RACE. Jones took eight minutes four seconds to coyer the full distance. Robinson eight minutes fifteen seconds, while Brown occupied exactly eleven seconds longer than Robinson, A CARPENTER’S DILEMMA. Find the centre of the right hand side of the rectangular part of the board, and nom that point draw a line direct to the apex, then draw anoiaer straight line from the same point to the left hand bottom corner of the board. If the board be cut along these lines, the three pieces will ca * )a^e formed into a A SPIDER AND A PLY. ? as ® ifc , ie curious that what appears to be the longer route is actually the shorter by two feet, as shown in- last week s issue. reJlitd E to A ' P ' B ‘’ H - M -~ Al^ady . W.C.S.G.—Thanks, and hope to know in due course that everything is quite all right again. Opoho. The explanation has been forwarded, and it is hoped that no difficulty wifi be found in following it. . X.Y.Z.—It might be worth while looking into again. TO CORRESPONDENTS. “ Amb'guoue.”—lt was clearly stated that all the nine digits are used once, and once only. You are quite correct as t T> to i Possibilities ” mentioned. J. R. Edwards.—That was the one most iiKely to be overlooked. Glad you found it. .V Without the rse of fractions it it is mipossiblo, obviously. K. J, G.’ —Very_ interesting, and will be tl looked into with view of using. F. L. W.”—A little obvious, perhaps, biit it can be elaborated somewhat. Thanks.