INTELLECT SHARPENERS

Otago Daily Times, Issue 21829, 16 December 1932, Page 15

INTELLECT SHARPENERS

By T. L. Bkiton.

Written for the Otago Daily Times

ARRIVED TOGETHER. Jones and Brown set out to walk from A to B and back, but did not start together, the former leaving A at a certain time in the morning, and Brown exactly 15 minutes later. The former kept up a walking speed of throe miles per hour right through his travelling time, and the other man maintained an even rate of four miles per hour. Both therefore must have arrived at the threemile post at the same time, and this was the only occasion the two men were together while travelling there and back. Jones rested 15 minutes for refreshments on the first half of the journey, at 8 a.m., and for three-quarters of an hour at 12.30 p.m. on the return journey. Brown, however, did not stop either on the way out or back, but tarried at B for two hours and three-quarters before returning, whereas his walking mate left B to return to A without any delay whatever. When the reader is informed that both walkers arrived back at A at precisely the same moment, he will doubtless agree that the details of the expedition now given are ample for him to decide the exact distance between A and B. TWO FOR THE ARMCHAIR. I have 104 counters on the table divided into five different heaps which may be called A, B, C, D, and E respectively. The difference between the numbers in A and B is exactly the same as between C and D, and between D and E. There are three times as many in A as in D, the C heap is twice that in E, while the combined numbers in C, D, and E are equal to the quantity in A. How many are in each? Each member of a grown-up family living in different parts of the Dominion sent a Christmas letter of greeting to the others. Each letter carried the minimum postage at the ordinary letter rates, but one was considerably overweight, and the total postage incurred on it was exactly four times the amount that was on each of the others. If the postal revenue benefited to the extent of 9s 5d by this correspondence, how many members of the family were there?

A NOVEL PUZZLE. Here is a novel puzzle that may give the would-be solver a fair amount of hard thinking for a moment or- two. A retailer’s code word for use as a private mark, indicating the cost prices of his goods, is one of 10 letters, all, of course, different, so that all the digits as well as the cipher may be represented by a different letter. The letters in the order of spelling this English word are the respective substitutes of 1.2.3.4.5.6.7.8.9.0., so that if the word happened to be “Logarithms,” an article whose cost price is 10s 3d would be marked LS/G, and so on. Using the word now under consideration the shopkeeper placed the private mark on an article, A/T, to indicate its cost price, and the selling price of it is 11a 3d, which represents 50 per cent, on the amount indicated by private mark. The cost price of another article is shown RF/L, and its selling price of 33s shows that 33 1-3 per cent, profit is made on cost. A third article marked as costing PB/- is sold (at a profit on that amount of 25 per cent.) for 22s 6d. What word .does the shopkeeper use as a private mark? A SET OF FOUR. Inquiries frequently come to hand asking the writer to settle some point of difference arising in argument, the most frequent type of question being that concerning probabilities or mathematical chances of certain things happening under stated conditions. Here is an interesting one. from “ Snooker ” which doubtless will interest more than those who indulge in the class of game suggested by the equipment mentioned — namely, a set of dice. Let it be assumed that each of a set of four dice is numbered in Arabic notation 1,2,3,4,5,6 respectively, instead of the usual form of indicating by spots the numerical values. Placing four dice together a four-figure number is shown on four different sides, none of which is the same obviously. “ Snooker ” asks how many different ways there are of arranging the dice in this way—that is to say, how many different numbers can be thus shown, without placing the same figure more than once in a number? Of course, Lie reader does not require to use pen or pencil to find this, and to make the question more interesting a condition may be added that the “six” may be turned upside down to make a “nine.” Can the answer to this be given rigjit off?

A CRYPTOGRAPH. The following string of 112 letters forms a sentence of 21 words of good English taken from a leading article. The subject is one of common interest and concern, and the method of. distinguishing the text is uniform throughout. There has also been followed a regular, and not in any way haphazard, plan of indicating the proper divisions between words, no guessing being necessary to reveal the disguised text if it is treated systematically, and if the reader can convert the passage within, say, half an hour, the time thus spent will have its reward in the solver’s mental exhilaration: —W 0 I J I F A DRMTVSKVUJWNISWH KAGVXTSISWJXIXY ICMKUCVXJWOIKMV BTIWJACVBIMKPUCI MOJOVNKARVWJPSL KGVDSWICARVWJCIB IPRKWOIJAVRTWTG PRKPTUIJVUKCDMM T P.

SOLUTIONS OF LAST WEEK’S PROBLEMS. AROUND MOUNT EVEREST. Twenty-three and a-half days. A straight ]OO would require SG days under the conditions. CLIMBING MOUNT EVEREST. 31185 feet would be the height of the mountain, based upon the figures recorded by the explorers. PAINTING A CROSS. The top of the cross would be four inches from the nearest edge of the zinc, and the end of the horizontal bar 14 inches from the side, similar distances on the other sides. AN ARMCHAIR POSER. Ten pencils at od, 10 at one penny each, and 80 of the lowest-priced ones at each. The condition that there must be the same number of two of the three kinds makes this the only solution. A CALENDAR PUZZLE. There are 13 years in the present century .in which 53 Saturdays occur, the first being the year 1904 and the last 1999. The next year of this happening will be 1938, then five years after that,

then six years twice, then five years after again, the succession being 6-5-0-6-5, and so on. ANSWERS TO CORRESPONDENTS. “Novice.” —(1) A scale of two inches to the mile would be found the most useful for your requirements. (2) From 27 to 33 inches is about correct or sufficiently so for the job you mention where time is more important than accuracy. J. H. D. —Thanks; very useful. G. E. F.—Yes, and of course it is obvious why the constant 2 is added.