Intellect Sharpeners

New Zealand Herald, Volume LXIX, Issue 21254, 6 August 1932, Page 5 (Supplement)

Intellect Sharpeners

MEASURING PROBLEM II t L BBXTOK Her® is a question In the form of at measuring puzzle that is somewhat different to the eight, five, three variety inasmuch that the " eight " measure which comes into use in most problems of this kind gives place to a four-gallon keg containing one-and-a-half gallons of wins., There are three vessels available for the operations including the one mentioned, the other two having the respective capacities of five and three pints, both being empty. Tho problem is to divide the contents! of the keg into three equal parts without waste using only the three vessels referrod to. We will assume that the three vessels were the property of three men, each possessing one of them, and that prtv vided the whole of the wine was divided equally betwe'%- the three, they were allowed to drink the whole or any part of the share that was to be theirs. It is obvious that as there was none of the wine to be wasted, at least one of the three had to consume part of his and allowing a "pouring" to be from one vessel to another or down a man'* throat, what is the smallest number, necessary ? AN ARMCHAIR POSER If the reader can answer this simple arithmetical question within the space of ten minutes without using either pen or pencil, it will indicate the possession of a clear brain, and the mental exercise he should derive from the effort cannot prove otherwise than beneficial. I went into a general store the other day and purchased several articles, tendering £3 in payment which exactly covered the expense in-i curred. Articles of different value were bought, some at one shilling each, some at two shillings each, while others purchased cost half-a-crown each. The question is to find the number of each kind of article bought with only the following few details to help the would-be solver in his effort. After purchasing a number of these goods at two shillings each, and exactly six times as many of the cheapest kind at one shilling each, I found that tho balance of the £3 could bay an even number of the most expensive kind at ; * half-a-crown each. This was done, the r whole of the £3 being thus spent, and 'I the question is how many of ench kind L were bought! The goods were crockery* ' LEFT AND RIGHT Hrre is a problem for the exercise of ; the reader's ingenuity, a puzzle which has the recommendation that it is not generally known and though it is similar to others that have appeared the solution is entirely different. Draw an oblong on a ' sheet of paper and divide it into seven equally sized cells each large enough for an ordinary counter. In the three lefthand cells place three coloured counters and in the right-hand cells three whito ones, leaving the central cell unoccupied-"" The puzzle is to transfer the two sets of ' counters so that tho white will occupy, the cells now in possession of the " reds -**■ and the latter to take their positions in the three cells on the right with the central one again vacant. The method of j procedure is as follows:—Each counter to . be moved only one, cell fit a time, but a counter may be jumped over another to an unoccupied space adjoining the latter, but not more than one counter may be jumped over in the same " move." The counter jumped over must adjoin the one moved* The coloured counters may only be moved to the right and the whites to the left. How many '"moves" are required? COMPARATIVE SPEEDS Two railroads run parallel between the townships " X " and " Y," the distance being immaterial. A train leaves " X**• for " Y " at precisely the same time as another on the adjacent line leaves " Y " for " X," both being non-stop. They run at their own speeds uniformly throughout, the train from " Y " owing to an engin® defect, being slower than the other for the whole distance. The train from "X "■ reached its destination at two o'clock and the other arrived at " X " exactly three hours later. The question is if the two trains passed one another at one o'clock, only one hour before the faster of the two reached " Y," can the reader say straight off and as <-non as the question is read over, what v. ere the speeds of the two trains! PENNIES IN BAGS " Curious " has sent an excellent problem that will require considerable mental alertness to solve, one that will need ingenuity rather than a knowledge of mathematics in order to arrive at the correct solution. Nine bags each contain a sum of money in pennies, all of different amounts. The bags when placed three in a row in the form of a square can be SO' arranged that the contents of any three of them in a line horizontally, perpendicularly or (eight directions in all), will add up the same amount which is less than twenty shillings. As " Curious " correctly says, there is no difficulty in making such an arrangement, but there is another condition which is the kernel of the puzzle. The contents of three bagij taken in any of the directions mentioned are to be equally divided between three children so that each one receives thi» same sum. With the consent of the sender of this problem and in order to limit the question to one correct solution it may be added that the sum contained in the bag with the largest number oi pennies addea to the contents of tho bag with the smallest sum total 6s 2d. Can the reader solve the puzzle ! LAST WEEK'S SOLUTIONS Only Two Examples.—-193, 384, 576 and also 273, 546, 879. Gold-Buying Problem.—l 4, 16, 18, 19 and 22 ounces respectivelv, the values being £B4, £96, £IQS, £ll4 and £132. Seating Accommodation.—There wem 1014 persons present, 507 men, 338 women and 169 children, ciited in 26 rows of 39 scats each. Gold, Silver and Copper Coins.—There must have been one-quarter broken off each coin which were then worth ninepence, twopence farthing and three fartilings each respectively. Much Debated Question. —None in tlie first year, ono tho second, one the third, two in tho fourth, three in the fifth, five in the sixth, eight in the seventh, thirteen in the eigth, twenty-ore in the ninth | and thirty-four in the tenth. ' ANSWERS TO CORRESPONDENT!! ) F.G.S.—Thanks for missing clause. ! F.E.M. —Posted regly in your addressed envelope. ' '* Weights."—Thanks for the particulars, ' which make the result obvious, i " Cones."—lt depends on the tendency r Of a body to take a position so that its i centre of gravity is as low as possible. « A.B.C." —Many mechanical tricks de--1 pond for ' their actions upon the same 1 principle mentioned. The other P Oll1 * 1 r ®" ferrod to concerns "Valperos attempt produce perpetual motion by the use M a magnet to raise an object which would MM afterwards fall by gravity. M