INTELLECT SHARPENERS

Otago Daily Times, Issue 23055, 4 December 1936, Page 3

INTELLECT SHARPENERS

Written for the Otago Daily Times By C- J. Wherefore

Correspondence should be addressed to Box 1177. Wellington

WORD CHANGE In the lines given below the spaces are to be filled with a series of words, each of which differs from the one before it by one letter, making the last word quite unlike the first, and with entirely the opposite meaning:— You see chis snapshot of a mountain scene, I the spot of which it is a view; Next Time I , next holidays. I mean, That's where I'll go and take my kodak too. Not much to about, for critics say By careless work I missed the chance I had, And I suppose they a truthful way, But still I'd to lose it, though it's bad. THE AGE OF A TREE A friend, who lives in the suburbs, drew my attention to a tree in his garden, and seemed amused when 1 was not able to say to which species it belongs. He informed me that he had grown it from a seed a number of years ago,—so many years, in fact, that the four numerals which form the number of that year when added together make the present age of the tree. The problem is to discover how many years old this tree is. Is it still a mere sapling, or should it be tall enough for my friend to sit under iis shade? ARMCHAIR PROBLEM "Last night three of the men in the hut were playing cards for small stakes, and several of us were watching the game. They were not dealing with amounts less than a penny, but even then the amount on the table was vory small. Well, since you ask the question, if I had the average of all three player's holdings, it would be only three times that of the man who had the least money. But this fellow quite unexpectedly "ound a coin, which had stuck in the lining of his pocket, and when ne had placed this beside his other money, he had one penny more than the holding which had previously been the largest. How much had each of the three men? "

TROUBLE WITH A BULLOCK . A man had to take a bullock out of a yard and drive it across a paddock to where there was a gate, through which he could put it into another paddock. The distance between the gate and the yard was an exact number of chains. When he had driven the animal a certain number of chains it broke back again a certain number of them before he could turn it. Owing to the fact that it broke back several times, he drove it forward several times, and each of these forward movements was one chain more than the one before it, the last being just enough to bring the bullock to the gateway. But those backward rushes were each in their turn one chain more than the one before it. and altogether the animal had run 44 chains by the time it was forced all the way to the gate. That is the problem, as it was given to me by my helpful friend, and I was rather suspicious. I asked whether it is not a painful reiteration of the very old story about the frog at the bottom of the well. On being assured that it is nothing of the sort. I professed to have solved it. " The gates are eight chains apart, and the animal always bolted the whole way back to the yard, after being driven five, six, and seven chains in the right direction, but the fourth drive of eight chains brought it the whole distance." My good friend objected that it is unreasonable to let the bullock get all the way back to the yard, so I had to search for another solution. What is the distance between the two gates, and what are the lengths of the forward and backward movements, which make up the long journey of 44 chains? EGGS One Saturday morning the manager of a grocery store drew the attention of one of his assistants to the supply of eggs left, and advised that they should be offered at prices which would get rid of them before the week-end. There were 17 dozen altogether, consisting of first grade at Is 3d per dozen, second grade at lid per dozen, and duck eggs, which were offered at a price midway between the others. At noon, when the shop closed, the last egg had been sold, and the amount received for them was just £l. When the assistant handed over a record of the different numbers sold, the manager said that there was an error of 2d somewhere, then he corrected himself, and blamed the man for writing the number 8, so that it looked like a 6. Did they sell half dozens of any of these three descriptions of eggs, and is it possible to discover how many of each kind there were?

SOLUTIONS OF LAST WEEK'S PROBLEMS Anagram.—Aspired, Praised, Despair. Time.—The professor came home at 2.6 a.m., the daughter at 4.3 a.m. Art Gallery.—There were 21, 3,6, 6, visitors on Monday, Tuesday, Wednesday and Thursday, respectively. Cyclists.—One man had 30 miles to go, the other 17 miles. A confus:ng problem, and yet the solution is easy, because it merely amounts to finding the L.C.M. of 2,3, and 5. Armchair Problems.—(l" The clue is that the amount quoted, 2s Bd, must be one-ninetieth of the whole price, which makes that price £l2. (2) It is clear that the village team made 64. The next larger square is 81, therefore their opponents beat them by 17 runs.