NUTS TO CRACK

Otago Witness, Issue 3995, 7 October 1930, Page 5

NUTS TO CRACK

By

T. L. Briton.

(For the Otago Witness.)

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

Solutions will appear In our next Issue, together with some fresh “ nuts.” Readers are requested not to send in their solutions unless these are specially asked for, but to keep them for comparison with those published in the issue following the publication of 'the problems OF SENSIBLE AGE. A little problem requiring only an elementary knowledge of arithmetic, though possibly one that may give the reader a moment or two’s quiet thinking, concerns two sisters, of whom one is of sensible age, though the younger has passed the “ flapper ” stage. The figures representing the age of the elder at the present time, happen to be those which denote the number of years that have elapsed since the younger girl was born, the figures, however, being reversed. Fourteen years ago No. I was twice the age of sister the second, and in the same number of years from now the former will be twice the age that the younger one is at present. If their combined ages now total one year more than six times their difference, and that “ now ” is the present year (1930), can the reader say in what year the lady of sensible age was born ? A RERFESHING PUZZLE. Both indoor and outdoor games always provide useful material for puzzleproblems, mathematical and othei kinds, and .here is one based on the game of dominoes, which most persons know how to play. Take five dominoes and arrange them in single file, horizonotally or otherwise,, so that the sum of the spots on the two end cards, as well as the sum of the three middle ones, is equivalent to an average of one spot per domino. With the small total of five, it might seem that a selection of dominoes for this purpose would be limited to the five lowest, virtually “ Hobson’s choice.” But that is not so for there are more than five cards from which the requisite number may be chosen. There are only four different ways that any five dominoes can be arranged to achieve this object, and to find them should prove an instructive as •well as a refreshing amusement. THERE AND BACK. A gentleman inquiring of a local rustic the correct distance between Te Monanui and Te Kara, was told in an enigmatical way, by relating the experiences of two cyclists, Smith and Brown, who had recently travelled the road there and back, though not in company. They both travelled in easy stages, and after the first day’s run' Smith increased his daily mileage by the same distance each successive day, completing the journey from Te Monanui to Te Kara in four days, and back over the same route in one day less. On the other hand, Brown rode the same distance daily, his respec tive “ runs ” being two miles per day more than Brown’s second day’s tally The gentleman seeking the information obviously could not find the correct di® tance from this statement, but as the rustic, in answer to a direct question, replied that Brown took exactly eight days to cover the distance there and back, the desired information was easily calculated. Can the reader say what it is?

WHO WON? A foot race reminiscent of the famous “ Dudeney ” problem, “ The Couple’s Con test,” took place between three student.’, and the information available concern ing it is quite sufficient to enable it to be solved, without taking anything for granted, as a number of readers did in the case of “ Cook and Gardener.” In the students’ race all started together off-scratch, the length of their strides being different, though each maintained his length uniformity throughout Y’s were half as long again as Z’s, and X’s .two and a-half times as long as the latter’s, though only one time and two thirds the length of Y’s. The last-men-tioned runner took five strides to every three of X, who made two to every five of the smallest boy Z. the latter taking three to every two of Y. It was only u short race of less than 100 yards, the course being marked in lengths of one foot. During the running, Y and Z hit the same mark together 25 times, X and Z 15 times, while X and Y landed on the same mark simultaneously on 10 occa sions. What was the distance of the race, and who won? MULTIPLIED OR ADDED. Can the reader find two numbers, either different or the same one repeated, which will give the same result when multiplied " as when added together? Quickly the reader will say two and two, which of course is an example of the curiosity." . But can. he supply any other examples, for the number is unlimited though not, as m the case of two and two, where the same number is repeated. There is an invariable rule governing this, and as it is useful to know, it will be published, next Saturday.;.. When it is known, a person will

be able, immediately upon someone suggesting a number of any value whatever, provide it is a positve one, to quote another number that will “ fill the bill.” In the meantime can the reader discover any two such numbers?

LAST WEEK’S SOLUTIONS.

TWO ALLIED POSERS.

The explanations given last week were limited to the bare statement that logically the clock, if its mechanism were in order, had to strike the hour, that is to say that the “ five minutes to go ” did actually expire. Also that the greyhound did actually reach the terrier in the time their relative speed indicated. The explanations could be amplified, but no doubt the reader will have sufficient matter to ponder over, and is recommended to read Herbert Spencer’s “ First Principles,” if sufficiently interested.

WEIGHING THE ’TOTS. Seven, nine, 11, 12, and 15 pounds.

WHEN ONE HUNDRED AND FIFTY. Sixty-two, fifty-six, and thirty-two respectively.

COMBINING THE POINTS.

P. 0.1. were coupled with T.N.S. respectively, their scores being 12 and 6, 9 and 9, 15 and 30.

ANSWERS TO CORRESPONDENTS. R. G. M.—Thanks for continued interest. The answer to the disputed point is that it applies in the one instance only. On the surface it would seem to contradict an established principle, but that is not so. “ Puzzled.”—The error is due to your having assumed the two lines to be of equal length, whereas the eastern side is one chain shorter. J. B. D.—Budget received with tfianks. L. E. W.—Yes, there was no alternative as top ’ and “ bottom ” indicated manner of packing.