Intellect Sharpeners

New Zealand Herald, Volume LXX, Issue 21520, 17 June 1933, Page 5 (Supplement)

Intellect Sharpeners

ET T. I» BRITON

MEN AND BOYS AT WORK ) I , i | ! i

A correspondent ** Colenso" has sent an arithmetical puzzle. Two men and five boys employed on levelling a 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 tho completion of the work was that only 10 days were allowed from the commencement by the original gang. The point raised by "Colenso" is, how many more men should bo put on the job so that it could be finished by tho end of tho 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 the first seven workers. Tho reader is recommended to first read the question carefully, otherwise he may be caught tripping. TWO FOR THE ARMCHAIR The foot of a garden ladder is leaning against the wall of a house, tho distance between the foot of it and the wall being exactly sft. The height of the top of tho ladder is exactly 2ft. below the sill of a window 14ft. from the ground, the wall, of course, being vertical. Can the reader say what is the length of the ladder? % The populations of the two towns X and Y at the end of the year 1930 are respectively 10,000 and 12,000 people. The former increased its numbers by 20 per cent annually since then. Tho 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 only a difference in the two" places of 120 people. What percentage was the population of Y increased in 1932? ATHLETES' RELAY TRIAL The following arithmetical puzzle has been received from " Beta:"—Two athletes were training for a " relay" race, the track used being circular in shape. The distance was once round 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 an hour. At that point Brown took tho 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, ho noticed that tho track ahead was some- • what boggy, and without checking hi* speed he ran direct to the destination mentioned, his uniform rate of running being 10 miles an hour. " Beta's" question is, if the full time occupied by both runners was exactly six minutes, what is the diameter of the circular course, assuming that the ratio of it to the circumference is seven to 22. " RESTORATION " PROBLEM Here is a "restoration" puzzle a little off the beaten track. Both the divisor and 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 tho 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 4 in the second place and a 3 in the last position. In the second position from tho left in each of the three subtraction lines are 4, 0, and a 3 respectively, and in the sum and the working there are 41 figures without repeating the " brought down" digits. Another help to the would-be solver is that tho digits in the divisor and the quotient added together make 22, The sum, of course, divides without remainder. One of this class of jmzzle will _ bo published weekly. WELL AND 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 being much simpler than the other he may elect to proceed without pen or pencil. Two pumps are employed in draining a well of water, tho larger of which discharges at tho rate of 100 gallons a minute, and the other 20 gallons less iu the same time. When the smaller pump works alone, the water sinks in the well at the rate of ono inch a minute, there being no soakage on account of tho walls of tho welj being of concrete. There are two questions arising from this statement, the first being 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' tako tho larger of thai two pumps to empty the well working alone, it being taken for granted that tho well is a full one? Tho suggestion that pen and pencil might be dispensed with is not. of course, a condition of the problem. LAST WEEK'S SOLUTIONS School Attendances. The average was 62.7. Question o! Salary. —" N's" salary was £l2O a year. Purchase of Land.—The areas controlled by Jones, Brown aud Robinson wero 564 acres, 1440 acres and 2301 acres respectively, before the transfer of certain portions between the partners. A Deal in Sheep.—The Lincolns cost the dealer £172 16s, and tho Romr.ey* £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. New Code.—The text is: " Bacon proposed a cipher in which each letter was denoted by a group of five letters which could bo used to separate words or to which he could assign separate meanings." 'lllO number of words in the text—3l in this instance—is always the key word, so that every message would probably have a different key. To get the equivalents of the letters write the alphabet-, letter for lettei, under the key-word. Thus the first I. T of the word "Thirty-one" would rej>resent either A, J or S. ANSWERS TO CORRESPONDENTS'. G.C.F.—Reply next week. " Alphabetical."—lt will be published on July 1. " Curious, You are quite right. The figures were correct as printed, but the . two denominations were traiuiposed. Thanks for comments: S.C.—The distance between the posts are in the order given - , onco around being 14 chains. (2) It is unusual to supply solutions of problems sent, uu* less they appear in this column.