INTELLECT SHARPENERS

Evening Post, Volume CVI, Issue 46, 1 September 1928, Page 31

INTELLECT SHARPENERS

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Readers with a little ingenuity■•; will find in this column an abundant store of entertainment and ■ amusement, and the solving of the problems should provide excellent mental exhilaration. While some of the "nuts" may appear, harder than others, it will be found that none will require a sledge-hammer to crack them. THREE HYPOTHESES. Three sheep-dealers, Acland, Boyd, ■■ and Cox, were discussing at breakfast one day in a certain township, the prices that their sheep were likely to fetch, the stock being yarded and ready for the auctioneer. Although each man had brought -in several classes of sheep, no one seemed inclined for soino reason to tell the others the exact number ho had. This much, however, was gathered from their conversation, and it might be sufficient for tho reader to discover for himself that tho numbers were. If A exchanged two rams with B for twelve ewes, the latter 'a stock would then total half as many again as A, or if A in a deal with C gave him two rams and twenty-two hoggets in exchange for forty-eight ■wethers, he, too, would then have half as many again as A. But if it came to a barter between B and C only, and B gave him thirty-eight lambs cor thirty-threo hoggets C would havo a total of only six sheep less than the combined number that A and B brought in. When the' reader is trying to find how many sheep each man brought, he should note that-there .are three distinct hypotheses/for- when, for' example, C and B are 'the operators all flocks are at tho time "in statuquo,", tho question being merely what would result if • any one of the hypotheses occurred? POSTAGE STAMPS. A correspondent, 0.W.C., -has sent a very interesting query concerning tho quickest method of separating" from ono another postage stamps in a long single strip, cutting or tearing along the perforations only. Although this is an age in which millions of pounds are being spent to save minutes, for to most of us "time is1 money," the object of submitting this", little query is Hot with the idea of showing, how the readers' minutes, and thereby his money, might be further saved, but merely because the puzzle offers an opportunity of testing his ingenuity. Here it is. If we go to a stamp vending machine instead of to the counter, we can, by putting., twenty-fivo pennies into the automaton got our stamps in a long strip. Having obtained them in this way the question is what is the minimum number of "tears" or cuts, necessary,to separate these along' the perforations into twenty-five singles? When tho reader is ready for experimenting, let him cut a strip of stamp width" from the margin of tho "Evening Post," but before proceeding delineate- it to agree with the usual stamp perforations; then go ahead. ANOTHER STAMP PUZZLE. The subject of postage stamps being one of every day discussion, here is a little problem that is liable to occupy the reader equally as long to solve as tho preceding one, but as both of them will be found entertaining the time will pass pleasantly. Draw, a six-, teen square (four by four), and take a number of counters .or their equivalent, representing stamps of one, two, three, four, and five pence each. The counters may be of any of _ these amounts desired, the object being to have a supply of each denomination on hand. It is required to place a counter on each of the sixteen squares so that the total of the whole lot makes four shillings and ' one penny exactly, the one condition being that not more than ono counter of the same value shall appear in the same direct line perpendicularly, horizontally, or diagon-; ally. It is possible to arrange them under the conditions stated, so that the board will show both more or less than 4/1 but there is only one arrangement of exactly this sum. THE BATTLE OF WATERLOO. Since the publication of the problem "When Captain Cook dropped anchor,"1 several readers have written to ask for a simple method of determining the day of the week of a remote date like the 2nd November, 1773, when Cook arrived off the entrance to Port Nicholson. Here is the method together with, a simple example. There are fifty-two weeks and one day in an ordinary year, and in leap year the same number, plus two days, and therefore in twentyeight consecutive years there are twenty-one ordinary and seven leap years, equivalent to 1456 weeks, .plus twenty-one days, plus 14 days, or 1461 complete weeks. Consequently any given date of a month will fall on the same day of the week in every twenty-, eighth year. This, however, does not apply when century years which are not leap years are included, 1800-1900 for example, and when making a calculation this should not be lost sight of. Let us take a case and ascertain on what day of the week the Battle of Waterloo was fought, the date being the 18th June, 1815. If we add 28 to 1815 a sufficient number of times to bring the year near the present one we will get to 1927, and from the Almanac we find that tfte 18th June, 1927, fell on Saturday. But as the period includes 190u, which was not a leap year, it makes a difference of one day, so the famous battle was fought on Sunday. Inter alia, it is remarkable what a large proportion of important events from tho Resurrection to modern times occurred on Sundays. THE OLD CALENDAR. And while on tho subject of problems concerning measures of time one of the questions asked by a correspondent is—"What is the purpose of leap years beside giving to spinsters a well deserved prerogative!" Well, the purpose can be explained and associated with a little problem, at the same time mentioning that Russia, by still adhering to the calendar of nearly two thousand years ago, gets more leap years than we do. Tho extra day in every four years was put in the calendar by Julius Caesar in 46 B.C. in order to make the ordinary year more nearly equal the actual time the earth takes to gi round the sun, called the solar year, of nearly 365 i days. But an extra day in every four years was rather too much, so a correction was made in 1582 by Pope Gregory omitting this extra day three times in every four hundred years, and that is our present calendar. Now for tho problem concerning the old style of reckoning. If in English-speaking countries the new calendar was adopted in 1752 and in that year the day after 2nd September was called tho 14th September, and that in order to make the necessary adjustments it was arranged that tho legal year should commence on Ist January instead of 31st March, how many days did those countries have in tho years 1751,i1752, and 1753 respectively, which all ended 31st December!