NUTS TO CRACK.

Otago Witness, Issue 3886, 4 September 1928, Page 14

NUTS TO CRACK.

By

T. L Briton.

(For the Otago Witness.) _ Readora with a llttl* Ingenuity will find in ils column an abundant ■tore of entertalnmer* and amusement, and the solving of the problems obould provide excellent mental exhilaration. While some of the "nuts" may appear harder than ethers, ft will be found that none will require a sledge-hammer to crack them. Solutions will appear in our next issue together with some -fresh •*auts.” Readers re requested not to send in their solutions, unless these are •Picially asked for, but to keep them for comparison with those published in the issue following the publication of the problems. THREE HYPOTHESES. Three sheep dealers, Acland, Boyd, and Cox. were discussing at breakfast one day 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 class of sheep, no one seemed inclined foi some reason to tell the others the exact number he had. This much, however, was gathered from their conversation—and it may be sufficient for the reader to discover for himself what the numbers were: If A exchanged two rams with B for 12 ewes, the latter’s stock would then total half as many again as A’s. Or if A, in a deal with C, gave him two rams and 22 hoggets in exchange for 48 wethers, C would then have half as many again as A. But if it came to a barter between B and C only, and B gave C 38 lambs for 33 hoggets, C would have a total of only six sheep less than the combined number brought in by A and B. 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 the time “ in statu quo,” the question being merely what would result .if any one of the hypotheses occurred.

POSTAGE STAMPS. A correspondent, “ O. W. C.,” has sent a very interesting query concerning the quickest method of separating from one 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 is money ” —the object of submitting this little query is not to show how the readers’ minutes, and thereby his money, n?ay be further saved, but merely to testing his ingenuity. Here it is. If -we go to a stamp vending machine instead of to the counter, we can, by putting 25 pennies into the automation, get 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 25 singles? When the reader is ready for experimenting, let him cut a strip of stamp width from the margin of the Daily Times, delineate it to agree with the usual stamp perfoi'ations, and then go head. ANOTHER STAMP PUZZLE. The subject of postage stamps being one of everyday discussion, here is a little problem that is liable to occupy the reader equally as long to solve as the preceding one, but as both of them will be found entertaining the time will pass pleasantly. Draw a 16 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 16 squares so ' that the total of the whole lot makes 4s Id exactly, the one condition being that not more than one counter of the same value shall appear in the same direct line perpendicularly, horizontally, or diagonally. It is possible to arrange them under the conditions stated, so that the board will show both more or less than 4s Id, 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” several readers have written to ask for a simple method of determining the day of the week of a remote date like November 2, 1773, when Cook arrived off the entrance to Port Nicholson. Here is the method, together with a simple example. There are 52 weeks and one dav in an ordinary year, and in leap year the same number plus two days. Therefore, in 28 consecutive years there are 21 ordinary and seven leap years equivalent to 1456 weeks plus 21 days plus 14 days, or 1461 complete weeks. Consequently,, any given date of a month will fall on the same day of the Exweek in every twenty-eighth year. This, however does not apply when century years which are not leap years are included—l Boo-1900, for example—and when a calculation is being made this should not be overlooked. Let us take a case and ascertain on what day of the week the battle of Waterloo was fought, the date being June 18, 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 June 18, 1927, fell on Saturday. But as the period in-

eludes .1900 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 the Resurrection to modern times occurred on. Sundays. THE OLD CALENDAR. While on the 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, it being mentioned at the same time that Russia by still adhering to the calendar of yearly 2000 years ago, gets more leap years than we do. The 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 go round the sun as shown in the solar year of nearly 365 J days. But as an extra day in every four years was rather too much, a correction was made in 1582 by Pope Gregory omitting this extra day three times in every 400 years, and that is our present calendar. Now for the problem concerning the old style of reckoning. If in Englishspeaking countries the new calendar was adopted in 1752 and in that year the day after September 2 was called September 14, and if in order to make the necessary adjustments, it was arranged that the legal year should commence on January 1 instead of March 31, how many days did those countries have in the years 1751, 1752, and 1753 respectively which all ended December 31 ? LAST WEEK’S SOLUTIONS. CHANGE OF A SOVEREIGN. As a person can hold £1 5s 9d in current New Zealand silver without being able to exactly change one sovereign, it is 5s 9d less than twice the amount that can be held when it is impossible to exactly change half a sovereign under these circumstances. This sum can be held in four coins. THE. COAL MERCHANT. The amount of the cheque sent by the Steam Laundry Company must have been £B4. A PECULIAR OCCURRENCE. As the problem did not say that the men were gambling in any form but merely “ playing ” for money, they could have been engaged as professional players in an orchestra at a ball for which they would receive money, and this is possible the explanation 'of the case referred to by the correspondent. AN ARM-CHAIR PROBLEM. The No. 2 train must have travelled on both days at half the speed of No. 1, viz., 15 miles an hour, though perhaps some readers may have decided that the correct answer was 10 miles per hour. Both trains were 660 feet long. AN EXCHANGE OF LANDS. As the four boundaries of A measured 100 chains in length, B 60 chains, and C 80 chains, Jones, as the new owner of B and C, had 40 chains more fencing to erect than Brown, though he had the lesser area by 21- acres. ANSWERS TO CORRESPONDENTS. R.T.C.—The “ feat-” demanding 20 moves had another condition attached involving “ A’s ” movements, but inadvertently omitted. “ C.”—Hardly agrees with the idea, as there are only two people concerned, the performance of one being “ plus ” that of the other; but your statement includes three “ ands.” ’ In any case, Grimshaw’s summary, according to one authority (A. H. Butt), gives a possible total of 81,896,864, which somewhat.dims all previous figures. W.C.S.G.—Thanks for the gallinaceous item. J.B. Much obliged and filed for future reference.