INTELLECT SHARPENERS

Otago Daily Times, Issue 22053, 8 September 1933, Page 4

INTELLECT SHARPENERS

Written for the Otago Daily Timet By T. L. Briton.

BY BOAT, TRAIN, AND CAB. While a party of people arranged a holiday trip from the city A, travelling to B and back, this little problem concerning the matter deals only with the outward trips, which were accomplished by boat, train, and car in that order of travel. The trip from Ato B may be regarded as a non-stop run, and any delay en route such as would be due to changing from one mode of conveyance to another may bo treated as negligible. One-tenth of the entire distance between the two places was travelled by launch which kept up a uniform speed of 10 miles per hour. One-fifth of the distance was covered by means of a " pickup" goods train which travelled at 20 miles per hour throughout to a point on the line where they were able to catch an express train. In this they were able to travel for a distance equivalent to one-quarter of the entire length from Ato B. The remainder of the distance to B was travelled by car, in which they speeded along to their destination at the fastest rate of travelling in the whole trip, namely, at 27 miles per hour. The whole journey occupied exactly five hours and thirty-nine minutes, and the question for the reader to answer is: If the express train travelled at four miles an hour faster than the poods train how far is it from A to B? This little problem being arithmetically very simple, perhaps the would-be solver may elect to tackle it without the aid of either pen or pencil. STOLEN APPLES.

W. J. B. has eent an arithmetical puzzle which in a less obscure form is Komewhat similar to the " Miser" problem published in this column some time ago. A boy entered an orchard without permission, and after he had eaten a number of apples filled hia poefcets with more of the fruit to take awa}', the number secured with this object being half as many again as the number he had eaten. Before, however, the lad had got over the fence again he was caught by the owner of the orchard. As the boy confessed that it was his intention to go into the adjoining scrub and eat the apples himself, the owner punished him In the following manner: There were four families living half a mile from the orchard, and to these places the farmer took the boy, who, of course, was compelled to carry the fruit. . To everyone in house number 1, the boy was made to hand an apple each, the number ob • sorbed in that way being half the. number he had plus half an apple. At houses numbers 2 and 3, visited in that order, the same procedure was observed with the apples that were left when arriving at each of the places. At the fourth and last house to which the orchardist and boy went, the remainder of what the lad had in his pocket was given, exactly the same method of allotment being observed as in the three previous instances referred to. The question asked by W. J. B. is: If the last distribution finished the number of apples that the bby had placed in his pockets, of how many did he rob the orchard?

THREE " AVERAGE " QUESTIONS. A stock dealer made a profit of £6O by: selling 12 draught horses at the rato of £4OO for 20. What was the average cost to the dealer of the animals sold? Of'a group of 30 people attending a recent race meeting some made a profit ■while some lost. If one-third of the whole party lost £6 each and half that number each lost £4, what was the average profit or loss of the whole party if the others who were winners made a profit averaging £5 each? In a certain. Rugby football competition the average number of points gained by the winners of the last nine matches was eight per match, eight of the results showing fewer points in each case than the average for the whole nine. Th.-> question for the reader to answer while sitting in his armchair, and without any aid in the form of either pencil or paper, is how many points were scored by the winners of the fifth match of the series if the average for the first four matches was seven and that for the last four contests five points? A "RESTORATION" SUM. A " restoration " puzzlo in the form of a sum in long division in which the quotient is a three-figure whole number with a one-figure decimal should provide the ingenious reader with a problem a litrla ofi the beaten track. There is no remainder, and of the 26 digits and cipher in the sum and working, excluding the decimal, 18 are missing, the absent figures being indicated by an X in every instance. x2 )x 8 x x (2xi decimal x x 4 x 4 x 1 x x x O x x 9 x x 6«x x 6 x A CRYPTOGRAPH. Here is a puzzle in the form of a cryptograph that should test the reader who makes an effort to translate the passage into intelligible English, which in its original text it is. As will be seen, the code consists of eight words of 15 letters in each. The method of disguising the passage is in the main original, though the idea is obtained from a plan of code writing adopted by the German army during the Great War. No scheme of substituting one letter for another will be found in the code, the problem of decoding being, first, to arrange these in 15 words of eight letters each, so that they will read, in their spelling order, the obscure passage in question, the whole construction following a systematic plan. PLIEIUAIOTHNUSG RYNRCLMNFTTTCIO EAGNEDEGFEHAHOB FCPTWWSRIREGANV ECORERSOVSAEDBI ROMASIAUEEDOIEO AROCHTGPLAVFVIU BDDTOEESECASINS. • SOLUTIONS OF LAST WEEK'S ' PROBLEMS. TWO FOR THE ARMCHAIR. (1) Thirteen without farthings and CG when they are included. (2) One shilling and fourpence and one shilling respectively. DIVIDING £SO 7s sd. There were 77 who participated, but had each received one of each of two denominations and four of the coppers with four of the threepenny pieces, the amount would be £53 5s 2d. DISCOUNT ON AN ACCOUNT. The amount of the account before any discount had been deducted was £4, the cashier having given a rebate of 2s instead of 3s, representing 2J and 3} per cent, respectively. ASCENDING A LADDER. Number the rungs 1 to 17 and proceed as follows whe,n the conditions eet out will have been complied with. Step to 1 then back to the ground. Then 1 2 3 and back to 2, then 3 4 5 and back