"NUTS!" INTELLECT SHARPENERS All rights reserved. (By C. J. Wherefore.)

Evening Post, Volume CXIX, Issue 98, 27 April 1935, Page 26

"NUTS!" INTELLECT SHARPENERS All rights reserved. (By C. J. Wherefore.)

Readers., with • little. Ingenuity will flnd'ln this coliimn an abundant >tor« «f entertainment and amusement, and the solving of the problemt should provide excellent mental exhilaration. While some oj me -nuts" may appear harder that others, it will be found that none - will require 'a sledae-hammer t« track them. Addrast eerreipendeoee te P.O. Bel 1177, Wei. llnaUß. , LAYING TILES. Two men, William and Harold, were sent to lay tiles in two hearths in the same house. Harold was the. quicker worker, and could set seven tiles while the other set six. They started at the same time, but twenty minutes later the contractor found that they were using the wrong tiles, and so would have to undo all the work they had done, and exchange the tiles which had been given to them. They set about pulling their tiles out, and in this they were able to work at the same rate, which was five times as fast as William could set them. How many tiles were still in position ,on-Harold's hearth at the time William finished removing his number? , . : , RAILWAY TICKETS. At a flag station a fairly large number of pasengers joined a train one , morning, and asked for tickets to a ' town not many miles away. Each one 1 handed the guard a coin of the same ! value, and should have received some , coins as change. The guard was well supplied with silver, but, had no copper coins, so that he could not give ' anything to any of these passengers, ■ but he promised to obtain it for them at the station referred to. This he forgot to do,.and apparently it was overlooked also by liis creditors, who had 1 distributed themselves in equal numbers over all seven carriages on the train. The result was that when his cash and his Ibookof tickets were examined the ; official who attended; to this found 'enough* money to account for ona ticket, more than had actually been issued from the flag station, and so looked through the book again to • see if W had counted them incorrectly.. ' How many, passengers, bought these tickets, and what' was the fate demanded? ./"■■■■■" ' ■■■■'.'" ' .' ' ' -'•■ •"' . SUBSTITUTION AND BOOK PUZZLE In the words .given below, numerals are to be written in place of the letters, so that the result is a sum in simple addition. No two letters have the same numerical value. The letters were derived from' the title of a book. To make a non-mathematical problem, change LIGHT into LIGHTEN, add AGfc, then shuffle all 18 letters and rearrange ; them to form the title of the book referred to. r SEAL .:. ..■■ GUNS ;-■ ". . LIGHT IS THIS A LARGE OR A SMALL " BOOK? A correspondent, writing from Nelson, asks for the,solution ~of the following problem. A. man was cutting the pages of a new book, and as it seemed a tedious task, a friend asked him how many pages there were. To ,this he replied: "If there-were 8 more, the number would be a multiple of 71, or. if there were 2 less, it would be a multiple of 73."" How many pages were there?. , ..... . , PURCHASE OF TWO BICYCLES. A boy wanted to. buy a bicycle, but had no money. The proprietor of the shop increased the price'by one-tenth of itself, and the boy undertook to pay this increased price in instalments of 1 three shillings per Nveek for '..a. given number of weeks. When his sister s,aw this bicycle, she! discovered that she required onevalsby and she bought one atVthe same shop, which: wag;marked with a price, half as much again as that taken by her brother. She had the advantage of possessing three pounds in the Post Office Sayings Bank. She drew all this, except three shillings, which she left as a precaution in case she-should not have the amount required (for ione .instalment.: in consideration Lof having - paid this deposit, she asked formless unfavourable terms. ' The dealer'increased'the price of her bicycle by- only the same number of shillings as he had charged her brother and he made her instalment of the same amount as'that which her brother . was paying., But the result"was that ' tha ■ girl •' had 'to pay ! instalments for one week longer.than her brother. What t were the cash prices of ; the two bicycles! aiid for hp.w many weeks did each purchaser, hiave to pay, these instalments?' ' ■'■'" •'.:■'""' \ '■'•■ '•'•■"■ " " ' ' ;;.' ;■■ -''-■■;'axtvAGE:-r .'. . , A fire" occurred in a small township, and as" the 'sniall wdoderi building which was used as the • library was threatened,1 the three .persons, A, B, and; C,: who acted, as honorary librarians, decided ;to 'carry all the books to another hoftse at;* safe distance. Now, A could i carry • only nine:.■ books at a time, but B, who found a small tray somewhere, was able to carry eleven, and C, who borrowed = a basket, carried- thirteen -on each trip 'he made.1 There'were1 a thousand books.to be ' removed,. -so that: it is ; obvious that these three librarians did not make the same-number of journeys,, but they felt quite sure that, the actual numbers did not .differ, very greatly from one another. What is the most 1 probable number of trips made by . each •of these. persons,; if it be understood that on no,trip did they carry more pr less.than the numbers described? V-;' ,' „ ;,; ', -~ : .; '■ -. ■; ~.. - '' '- "." ■'"■;].\ 'SOLUTIONS. .. ' :■■.-■ •■ . • ''Trams . and' Pedestrian;— Three and nine-seventeenthsof a mile per hour. ,-■ Fruit Grower.—There were 361b in each case, and'they-'were sold at one penny per Ib. ■ -' . Collection.—The point is that the number'of; threepenny pieces could not be more than 75 or less than 71. Ethel ■ collected the smallest number of them, and it follows that she had four halfpence in her box. " ,'■'-.. ■"■ Deteclive, Story.—Add together the 721 and the 9, then-half this sum equals 365, which shows the three numerals, but not necessarily in correct order. Hence there are six ways of grouping; them, 653, .635, 563, 536, 365,' and 356. The first and third are primes, the second and fifth are multiples of 5, and the fourth is a multiple of 8. Therefore the last, 356, is the .number of the taxi required. From Overseas. —The problem in this form • can only, mean that the ship is 126 years old, and was fitted with i a new boiler 63 years ago. The problem from which' this seems, to be copied stated'that. 63 is the sum of present ages, and that present age is twice that of boiler at the time when the ship's age was equal to present age of boiler. To this, of course, the answer is that the ages are 36 and, 27. .