NUTS TO CRACK

Otago Witness, Issue 3958, 21 January 1930, Page 65

NUTS TO CRACK

by

T. L. Briton.

(Fox thi Otago Withim.) Readers with a little Ingenuity will find in this column an abundant store of entertainment and amuse, ment, and the solving of the problems should provide excellent mental exhilaration. While some ot the " nuts ’’ may appear harder than others, it will be found that none will require a sledge-hammer to crack them. Solutions will appear In our next Issue, together with some fresh “ nuts." Readers are requested not to send In their trlutions, unless these are specially asked for. but to keep them for comparison with those published in the issue following the publication of the problems. THE BIRTH OF CHRIST. Curious” writes:—“Some time ago you published a problem entitled “ When Captain Cook Dropped Anchor,” inviting readers “ to find on what day of the week the great discoverer anchored off Barrett’s reef, his log book showing it to be the 2nd November, 1773. Will you please publish the method of calculation, as we have had a discussion as to the day of the week upon which Christ was born?”

ell, the method would not be quite the same in that ease, nor in fact for any period prior to the Gregorian mode of reckoning, which was first adopted in England in the year 1752. Nevertheless we can have a little problem on this interesting point by assuming that the present calendar existed then. The year in which Christ was born was of course 8.C., but the calculation may be made 7rom the first of January, A.D., 1, and the day of the week for the previous year adjusted accordingly. For problem purposes century leap years may be ignored throughout, for there have been none since the Gregorian calendar was adopted. Under these conditions what day of the week was it? The method of calculation will be published next week. UNCLES MATHEMATICS. Uncle Dick, having promised to buy some marbles for his four young nephews, sent Harry to ascertain the prices and details of the different varieties on sale When the boy returned with the necessary particulars, Uncle sat down to make a calculation, after which he handed the boys a certain sum of money to be wholly expended in the purchase of four varieties of marbles, the nephews to receive the same number each, irrespective of price. Let us assume that another condition was imposed besides the one mentioned—viz., that the total sum expended was an even number of pence, and with these stipulations the reader should enjoy finding what was the actual amount that the marbles cost uncle. The details that Harry obtained were that “ crystals ” could be bought at the rate of five for twopence, four of which were worth five “clays”; three “agates” were the monetary equivalent of seven “ crystals,” whilst eight “ pebbl ; ” were worth as much as 15 agates. What did the marbles cosC if the price for the lot was the smallest sum possible under those conditions? A MILE WALK. Hopkins and Tompkins take their recreation in walking tours, but have kept no records. It is known, however, that the former is a slightly faster walker than his companion, for although they always start off in company and return together, Tompkins may always be seen tramping behind the other after they have travelled a few miles. Let us have a little problem on the point in order to ascertain their relative speeds, and assume that Hopkins takes a minute more to walk 13 miles than Tompkins takes to travel 12 miles. At these rates can the reader calculate how long each tramper takes to walk one mile, if, starting together and maintaining their respective speeds throughout, Hopkins beats his companion by one minute? It is a simple calculation. A LONGER TOUR. Whilst on this subject, reference niav be made to a longer tour by these two walkers during a month's vacation they took at Christmas. In finding the answer to the question which follows, the reader will of course ignore their record as revealed in the preceding problem and be guided only by those now stated. Both men started together from the same place, travelling in the same direction, and walked uniformly throughout at different rates. After nine days Hopkins was 72 miles ahead of Tompkins, when he turned and retraced his steps, travelling back for a distance equal to that which would take the other man nine days to accomplish, and passed his companion en route. If Hopkins at that point turned again and overtook Hopkins in exactly twentytwo and a-half days from the start, what was the daily’ rate of walking of each man ? A USEFUL "AVERAGE” PROBLEM. Here is a practical question in " averages ” of a kind often met in that particular class of business, for, whether it be * boarding house, a military barracks, or aught else, the principle involved is the same. In this ease it is a boys’ boarding school, where careful records are kept. The average number of lads in residence last year was 25, which

is five fewer than the school’s normal residential capacity. The statistics kept by the house master show that an addition of five boys to Jjie normal strength increases the gross yearly expenditure by exactly £3OO, but diminishes the average cost per head by £l. From these details can the leader find what the annual expenses are when there are 30 boys in residence? LAST WEEKS SOLUTIONS. EMPIRE-MADE GOODS. The importations would require to increase by two-thirds (66s per cent.) in order that the Customs revenue may not suffer by the reduction in the tariff of 40 per cent. A WELL-BORER S TENDER. The tender was for £2700. BUYING PIGS. Dan Callaghan and Fred Aldridge. ANOTHER PUBLIC CLOCK. The regular interval between the strokes was five seconds ignoring fractions. A CLEAR STATEMENT. The net profits for the year being £412 10s, the insurance premiums represented 71 per cent, of that sum. The reader will, of course, note that £3O 18s 9d had been included in expenditure before the profits were declared.

ANSWERS TO CORRESPONDENTS. “ Solar.”—The actual difference is decimal 2422414 of a day, practically 5 hours 48 minutes 49 seconds. Hence the correction by omitting a leap year three times every 400 years, which has brought the solar and common years more in agreement, the bissextile once in four years making an even six-hour difference. Problems involving both calculations have already appeared.

“Pax.”—Your friend wins the wager, as the Peace Treaty was uot ratified until January 10, 1920, though the Armistice terms were accepted by the Germans on November 11, 1918,