INTELLECT SHARPENERS

Otago Daily Times, Issue 21544, 16 January 1932, Page 18

INTELLECT SHARPENERS

By T. L. Briton.

Written for. the Otago Daily Times,

“I FOUND IT.” Here is a little poser which should interest the reader, and particularly the lover of cbuuter-moving puzzles. Make a diagram of the dial of a time-piece, omitting the hands and also the hour numbers 2,4, 8, and 10; and draw four lines direct from the centre to the hours 12, 3, C, 0. Then take eight counters and mark each with a letter contained in the words “ I found it,” distinguishing the capital and small “ i.” Place the capital I counter on the hour 12, “ f ” on the 1, “ u ” on the 3, “ t ” On the 5, “d ” on the 6, “ o ” on the 7, “n” on the 11, and the small “i ” at the x centre, The puzzle is to arrange the counters under the following conditions, so that the letters form the words “ I found it ” reading from right to left, the centre being then vacant. The counters should be moved one at a time to or from any position to one adjoining if unoccupied, and when moves are being made to or from the centre the counters must travel along the lines prescribed. They may be moved in the same direction, or opposite to that taken by the hands of a clock, except, of course, the moves to or from the centre, to which that condition could not apply. A counter may not be “jumped” over, nor may two occupy the same postion at the same time, and one of them must not be moved at all. The'reader should note the word “ adjoining,” and if he can achieve the desired result in fewer than 17 moves, a record will have been made.

UTILISING THE SPACE. The problem concerning a method of economical packing which appeared recently, has prompted " New Reader ” to send along the following which is arithmetically very simple, though at first it may not appear so. A quantity of gold bricks was being packed in boxes of equal capacity, and the size of them is what the reader is asked to determine from the following information concerning the metal slabs which, when packed, utilise all the space available, their uniform size being 12 J inches in length, ] I inches wide, and one inch thick. The question is: If it is required to pack these into rectangular boxes of uniform size in such manner that not more than 12 are laid on their edges, what should be the inside measurement of a box having equal length and breadth if 800 of the size stated are packed into it and utilise the whole of the space? This is quite a useful question, and to find the particular method of packing under the prescribed conditions should afford the reader the opportunity of exercising his ingenuity, though the arithmetic of it is very simple. j STUDYING ECONOMY. Sam Loyd was probably the first of modern problem-makers to formulate a puzzle concerning the remaking of a broken chain, and here is one of his improved by H. E. Dudeney, the wellknown London Mathematician, which should give the reader a few moments of hard thinking. A chain of 60 links in the form of a necklace is broken into nine 'distinct parts as follows:—Three pieces each containing six links, another with three links, another with four links, two with five links, one piece with seven links, and the ninth piece with eight links —total, 50 links. A working jeweller offered to remake these into the original form of the endless chain, though the links would not necessarily be joined to the actual ones as before, and to charge for the work at the rate of 4d to open a link, and 8d to close it. Before the owner accepted the offer, he ascertained that a new one of the same size could be purchased at the rate of 2d per link, namely, for 8s 4d. On the assumption that, when mended, the old chain would be equal in all respects to the one purchasable at the price stated, can the reader find which would be the more economical transaction to the owner?

FOUR BROTHERS. A keen problem-lover, C. J. W., evidently does not allow his annual furlough to Werfere with his interest in this column, for he has sent the following little problem from his holiday resort. It is, in one respect, similar to others received from this correspondent, in that “finding the way” requires the hard thinking rather than “ travelling the route.” Matthew, like his three brothers, two of whom are younger than he, has not yet reached his fortieth birthday, and the number representing his age in year to-day is the product of two whole numbers. If those two numbers are each reduced by two, their product would represent the age of Matthew exactly 18 years ago, strange to say, these details are also true concerning the ages of the other three brothers. Can the reader find from these facts the respective ages of the four people? Possibly many would-be solvers will scorn the use of pen or pencil in finding the correct answer, though the sender of the problem does not stipulate this. FOR THE ARMCHAIR. No doubt the reader who sought the assistance of either pen or pencil in solving the previous problem, will ignore their aid for this one. It is not difficult in any way, and C. J. W. describes it correctly when he states that the answer should be obvious after a couple of minutes’ thought. Every afternoon in the week a guide accompanies a party of tourists to one of the scenic attractions not far from the hotel where they reside. The party travels there and back in a bus driven by the guide, and the fare charged for each person is at the rate of one penny per mile travelled in the vehicle. Recently the guide was given a month’s holiday, and during his absence another man drove the bus, and in that period of duty the substitute driver collected fares at the rate mentioned to the amount of £l7 3s 7d. As only one trip there and back was made daily, and as every seat was occupied on every occasion, what is the distance from the hotel to the spot referred to?

SOLUTIONS OF LAST WEEK’S PROBLEMS. AN EXAMINER’S POSER. Two men in addition to the four already employed would complete the work in an extra day. The examiner sprinkled the problem with a little humour, as the boys contributed nothing to the results. FITTED EXACTLY, From a point on one side three inches from the top corner cut four inches parallel to the top, then four inches parallel to the long sides. Repeat these two cuts, and make a final one of three inches parallel to the top. The two pieces will be found to fit and make a board one foot square. A SQUARE WITH CIRCLES. If the four pennies are placed heads down on the table, they can be so arranged that the four linos above the dates will form a square. ONE FOR THE ARMCHAIR. The first day of a century cannot fall on a Wednesday. PAYMENT IN KIND. Seven received 30 cases each, and the eighth 40 cases from the total of 2000 cases.