Now Supposing

Sun (Auckland), Volume 1, Issue 21, 16 April 1927, Page 12

Now Supposing

Some Intellect Sharpeners

(BY

T. L. BRITON.)

Readers with a little ingenuity will find in this column an abundant store oi 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. Readers are requested not to send in their solutions, unless these are specially asked for, but to keep them for comparison with those published on the Saturday following the publication of the problems.

A FARMER, not adept at figuring, usually counted on his fingers, and acquired a habit of tallying In fives. He was preparing a box of eggs for the market, and counting them in this way, found that there was one over. As he desired the quantity to be an exact number of dozens, and didn’t quite see how it was possible counting in this way, he caller the lad to help him. The boy first counted them two at a time, then in threes, and found one over each time. The next lad then tried his hand, counting them carefully first in fours and then in sixes, and strange to say that in each count there was again one over. The farmer's wife, who nad been patiently waiting in the cart, then came along, and counted them straight off in dozens, finding that the number over would divide without a remainder, into the original number of eggs. The even dozens were then placed in the market box, which, when full, would hold 40 dozens. What was the number of eggs originally? The Snail. Sam Loyd, as most readers know, was perhaps the best of modern problem composers and puzzle authors, his work covering every variety of problem in indoor games of science and skill, particularly chess, and he originated unlimited pos-ers in the field of mathematics. Yet in the old problem of*the snail, his solution was not acceptable to most thinking people, and caused much opposition and controversy at the time. The wall was 12 feet high, and the snail, starting from the ground, climbed four feet every night, dropping back three feet everv day. How many days and nights did it take to reach the top? Loyd's curious answer was based upon the actual tim e of starting, but it is difficult to see why. for the mollusc being on the ground couldn't travel either way until night fell. If, however, Its starting point were, a distance above the ground, Loyd s solution could be followed. His answer will appear next week with the more acceptable one.

County Cricket. None of the selected team for England were engaged in the county match which the writer umpired recently,' but It would 1 have been in teresting t c see how out champion batsmen would have shaped on that wicket. The knobs and holes however, that covered the greater part of the pitch, did not prevent those sturdy country lads from putting up quite respectable scores. The teams represented the adjoining districts of K and M . the former winning by four run 6. Looking at the book afterwards, the scores revealed some interesting features, so a note was made on them. K batted first ana made the highest-innings score of the match, M following with onefifth less, but th e latter's second effort produced one-fifth more runs than K's second innings. Another feature was that M’s first exactly equalled

K’b second innings. What were the scores in the match? “Fifteen-Sixteen.”

Here are two capital little patience problems, one based on the rules of cribbage, the other providing another form of counting. Take the cards one to nine and try to discover in what order they can be placed on the table in three rows, so that horizontally, vertically and diagonally, they will count fifteen, thus scoring as it were sixteen (16), —“fifteen-sixteen.” In the other the same cards are used and the problem is to place them on the table in the form of the letter T, so that the spots in the horizontal row will exactly equal those in the upright. There will of course be five cards in each, because by placing five in the top line, the centre one will also form one of the column and counts in it. Ther e are quite & number of different ways that the cards can be so arranged, and it is an entertaining problem to discover how many. Mixed Numbers. Two mathematicians, Edouard Lucas, a Frenchman, and Ernest Dudeney, an Englishman, vied with each other in discovering new problems and curiosities in mathematics, and usually, honours were easy between them. But the Englishman scored against his rival when the latter in one of his publications asserted that there was no way of expressing 100 in the form of a mixed number having only one figure in the integral part, and using all the digits, one to nine, once only. They agreed that there were 10 different ways of expressing this with two figures in the whole number, but Mr Dudeney showed an instance, the only one, where a mixed number can be written (expressing 100), which contains all the nine digits once onl>, and with only one figure in the whole number. Here is one with two figures in th e integral part, 82 and 3546 over 197. but can the reader discover the solitary instance where one figure takes the place of 82 under the condi tions stated? LAST WEEK’S SOLUTIONS. The maid was 20 years of age anu the youngest four, with seven children between, born at intervals of two years. The problem read “four times older,” which is equivalent to “five times as old.” I wonder how many readers solved the problem, for the difference between the two phrases is | frequently overlooked e v « n by experienced writers. At the Pictures. The gentleman bought 10 tickets at half-a-crown each, 10 at sixpence each and SO at threepence each, spending two pounds ten shilling for one hundred seats, the same number being in two classes. The Lapse of Years. Nine and three-fifths years must have elapsed between the two events mentioned. His Income. Jones’s income was £270 per annum. In the two years therefore £252 was spent in the manner stated, leaving £2BB in the bank. Tendering Small Money. It will perhaps surprise the reader to know that the exact sum of one shilling and elevenpence can be tendered in current New Zealand coin in more than five thousand different ways.