INTELLECT SHARPENERS.

New Zealand Herald, Volume LXIV, Issue 19720, 20 August 1927, Page 5 (Supplement)

INTELLECT SHARPENERS.

JiX X. L. BRITON". * Readers are requested not to send in their solutions unless these are specially following the publication of the problems, asked for, but to keep them for comparison with those published on the Saturday A FLOOD RESULT. A large cellar, 500 cubic feet in size, was flooded to within 50 gallons of overflowing, and had to be pumped out by manpower. Moro than half the water was emptied the first day, but owing to the percolating nature of the soil, there was twice the quantity in the cellar next morning as the men had left. The second day the same quantity was pumped out as on the first occasion, but next morning there was three times as much as had been left the night before. On the third day a similar quantity was again got rid of, bat the morning revealed four times as much as the men had left the previous evening. The same daily quantity was got out on the fourth day, but next morning just five times as much as had been left was found in the cellar. By pumping out on the fifth day exactly the same quantity as on each previous day, the men managed to finish the job. How much water was in the cellar when they started pumping ? A BEQUEST. Two charitable institutions shared a bequest of £4OOO, one of them, the hospital, receiving a larger portion of it than the other. Both beneficiaries invested the money, but the hospital committee was not as fortunate as the other body in the matter of interest, the latter securing an investment yielding two per cent, more than the hospital. The first year the joint earnings in this way amounted to £268. If, however, the rates of interest had been reversed, the two investments for the 12 months would have yielded in interest £292. How was the bequest of £4OOO divided between the two institutions ? BROKEN TIME. A skilled mechanic, working in a brass foundry, received wages at the rate of 4s an hour. He was, however, very irregular in the hours worked, owing to doing outside jobs on his own account. When the manager hinted to him that he must put in more time or lose the job, the mechanic offered the following proposition, which was accepted. He agreed to give regularly more than half of the usual trade hours to foundry work, which, in this establishment were 48 a week, | the rate of pay to be 4s an hour, with a forfeit of 5s an hour for all time away during working hours. He made his proposal cn the basis of being able to give at least three-quarters of his time to the foundry, but on pay day at the end of the first week, he was only entitled to receive 7s 6d. How many hours did he work ?.

UNORTHODOX CROSS-WORD PUZZLE

Although readers have, not infrequently, written to say how much more this column is enjoyed than cross-word puzzles, one of the latter is being included this week, solely because it -is somewhat different and not belonging to the orthodox variety of cross-word problems. As there are no "blocks" in the puzzle, each square being required po contain a letter of the desired words a diagram will not be necessary. Down. 1. To vex, to annoy. 2. Parts of the human body. 3. Contained in a furlong. 4. Grocers stock them. Across. 1. To fall into a sloping posture. 5. To raise one end of. 9. A thrust. 13. An awning in a boat. BOWLING AVERAGES. A little probltai published- some time ago, concerning the average rate of speed for a complete journey, that a motorcar makes if it runs at a uniform rate of 20 miles an hour on the outward trip, and 30 miles an hour returning over the same road, gave rise to much controversy. A lady who raised the question was met with the answer that the average speed for the whole trip was undoubtedly 25 miles an hour. But then is it not a fact that large societies as well as numbers of individuals exist to-day who contend that the earth is flat ? A more perplexing little puzzle that speed averages is one concerning possibilities which are likely to face one when working out bowlers' cricket averages. For no doubt the reader can discover an example in which a bowler A obtains a better average than B in e3ch of the two innings, yet the latter comes out with the better average for the match.. Why ? It is worth pondering over? LAST WEEK'S SOLUTIONS. On the Highway. B must have beeD 25 miles from the city when A arrived there. A School's Enrolment. In the five standards, 11., IH., IV., V,, and VI. there must have been respectively 7, 14, 15, 24 and 20 pupils. Discs and Solid Spheres. % 1. Thero is no difference between the number of discs and spheres under the conditions stated. 2. The square of tha diameter of a sphere multiplied by a certain factor gives the . area of thai, sphere's surface, and the cube of the diameter multiplied by one-sixth of the samaf factor gives its volume. Obviously thert the diameter in the problem must have been 6in., and it is immaterial what thd factor is. Counting Sovereigns. If the eight bags contained, respectively If the eight bags conained, respectively 1, 2, 4, 8, 16, 32, 64 and 73 sovereigns, any sum required from one to two hundred can be paid by giving one or mora bags, none, of course, being duplicated. ! Scotland Yard's Problem. I There are several times in 12 hours when the hands of a clock are together, and jas the time required by the problera was between midnight and two a.m., the watch must have stopped at 5 minutes 27 3-11 seconds past one a.m., the hands being taken together.