INTELLECT SHARPENERS

Otago Daily Times, Issue 21981, 16 June 1933, Page 2

INTELLECT SHARPENERS

Written for the Otago Daily Timee. By T. L. Bkixon. MEN AND BOVS AT WORK. A correspondent, “ Colenso,” has sent a little arithmetical puzzle, which, he says, “ is on all lours with the notorious problem set at an entrance examination at the University some little time ago, about the fairness of which there was considerable controversy.” Speaking from memory, 1 think that “ Colenso ” is a little astray in this, but as the one he sends is very suitable and interesting here it is. Two men and live boys employed on the levelling of an area of ground intended for tennis courts completed one-half of the job in six days. One extra man and another boy were then put on to assist and one-third more was done in three days. The time limit for the completion of the work was that only 10 days were allowed from the commencement by the original giuog, and the point raised by “ Colenso ” is, bow many more men should be put on the job so that it could be finished by the end of the tenth day? Of course, it may be taken for granted that the extra men and boys put on the work maintain the same rate of progress as shown by t,he first seven workers. The reader is recommended to read the question carefully, as otherwise he may be caught tripping. TWO PUMPS. While it is not anticipated that the reader had any difficulty in quickly finding the correct solution of the preceding puzzle, here is one involving precisely' the same principles, and as it is much simpler than the other he may elect to proceed without extraneous aid in the term of pen or pencil. Two pumps are employed in draining a well of water, the larger of which discharges at the rate of 120 gallons per minute, and the other 20 gallons less in the same time. When the smaller pump works alone the water sinks in the well at the rate of one inch per minute as a result, there being no soakage as the walls of the well are of concrete. Two questions arise from this statement. The first is, what depth is the well if both pumps working together can pump it dry in exactly two hours? The second is, how long would it take the larger of the two pumps to empty the well working alone; it being taken for granted that the well is a full one? A “RELAY” CONTEST. The following interesting arithmetical puzzle has been received from “ Beta,” and the reader will probably find that the solution of it ig sufficiently obscure_ to give him a few moments of serious thinking. During the recent wet weeks two athletes were one afternoon training for a “relay” race to take place at the annual sports meeting, the track used 'being circular in shape. The distance was once around the centre of the track, and in a “trial” between the two runners, Jones, who started first, ran half the distance at a uniform rate of 12 miles per hour. At that point Brown took the staff carried by Jones, and, without any perceptible delay carried on the running. But when the latter had travelled exactly two-thirds of the distance to the point from where Jones had started, he noticed that the track ahead was somewhat boggy, and, without checking his speed, he ran direct to the destination mentioned, his uniform rate of running being 10 miles per hour. Beta’s question from these few details is: If the full time qccupied by both runners was exactly six minutes, what is the diameter of the circular course, on the assumption that the ratio of it to the circumference is 7 to 22? TWO FOR THE ARMCHAIR. The foot of a garden ladder is leaning against the wall of a house, and the distance between the foot of it and the wall is exactly five feet. The height of the top of the ladder is, exactly two feet below the sill of a window, fourteen feet from the ground, the wall, of course, being vertical. Can the reader say what is the length of the ladder? The populations of two towns X and Y at the end of 1930 are respectively 10,000 and 12,000 people. The former increased its numbers by 20 per cent, annually since then, and the population of Y at the end of the year 1931 showed that it had increased by 10 per cent., and at the end of the year 1932 there was a difference between the two places of only 120 people. Can the reader find from these few particulars by what percentage the population of Y township increased in the year 1932? A “ RESTORATION ” PROBLEM. There have been numerous inquirers concerning this class of puzzle. It is not always possible to include more than one “ Restoration ” problem each week, as requests are on file and are frequently being received from readers who favour puzzles of a variety of kinds that make quite a formidable list. But one of these interesting problems which give excellent opportunity for the reader to exercise his/ ingenuity and reasoning powers will be published weekly. Here is one a little on the beaten track. Both the divisor and the quotient of a long division sum contain four digits each and the dividend seven figures. All the figures of the divisor are missing, and the first and third figures of the quotient have also been deleted, reading from the left. From the dividend all the digits' in the odd places are missing, the other three figures reading the same way being 7,9, 2, and the seven figures if added together total 36. The available two figures in the quotient are a 4 in the second place and a '3 in the last position. In the second position from the left in each of the three subtraction lines are 4. 0, and 3 respectively, and in the sum and the working there are fortyone figures without repeating the “ brought down ” digits. Another help to the would-be solver is that the digits in the divisor and the quotient added together make twenty-two. The sum of course divides without reipainder. SOLUTIONS OF LAST WEEK’S PROBLEMS. SCHOOL ATTENDANCES. The average attendance for the week was 62.7, TWO FOR THE ARMCHAIR. The respective answers are 6 and 18 different ways. A LAND PURCHASE, The areas controlled by Jones, Brown, and Robinson were 864 acres, 1440 acres, and 2304, acres respectively ‘before the transfer of certain portions between the partners. A DEAL IN SHEEP. The “Lincolns” cost the dealer £172 16s and the "Romneys” £129 12s, both lots being sold for £352 Bs. There were 576 sheep altogether, but under the alternative proposal he would have received 588 sheep for the same money. A NEW CODE. The text is:—“ Bacon proposed a cipher in which each letter was denoted by a group of five letters which could be used to separate words or to which he could assign separate meanings.” The number of, words in the text (“ thirty-one ” in this instance), is always the key word, so that every message would probabjy have a different key. To get the equivalents of the letters write the alphabet, letter for letter, under the key-word. Thus the first “ T ” of the word “ Thirty-one ” would represent either “A,” “ J,” or “ S.” ANSWERS TO CORRESPONDENTS. S. C. — (1) The distances betiween the posts are in the order given, once around being 14 chains. (2) It is unusual to supply solutions of problems, unless they appear in this column. “ Curious."—You are quite right. The figures were correct ns printed, but the two denominations were transposed. Thanks for comments, “ Alphabetical.”—lt will be published on