NUTS TO CRACK

Otago Witness, Issue 3994, 30 September 1930, Page 23

NUTS TO CRACK

By

T. L. Briton.

(For the Otago Witness.)

Beaders 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." Beaders 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. TWO ALLIED POSERS. These two questions, submitted by the correspondent, “A. C.,” were published on the 23rd of last month, and numerous comments have since been received from readers. Let us take the “ Greyhound ” and “ Terrier ” problem first, which, as an interesting correspondent, “ L. E. W.,” says, is easier of explanation. Both problems, as he states, fall into the same category, each being an example of the logical fallacy known by the Latin designation, “ Ignorantio elenehi,” or, in other words, the logical fallacy of arguing to the wrong point. As hinted when stating the problem, it is one of the earliest recorded mathematical fallacies, and dates back many centuries, the Greek “ Sophists ” referring to it in the form known to most readers as “ Achilles and the Tortoise.” But to this particular question. Using the word “ overtake ” in the sense of “ run as many laps,” the example of the greyhound and the terrier appears to prove that the former will not overtake the smaller dog while running three plus one plus one-third plus one-ninth plus etc. laps, that is to say, that he will not overtake him till he has completed the'sum of the series, which is four laps and a-half. In reality, however, what is proved is that the faster animal will pass the other between the fourth and fifth laps. In other words, when the greyhound has run four laps and a-half he will have run as far as the smaller dog, plus the latter’s three laps start. The other question sent by “A. C.” involves the same principle as the dog problem, but is unlike it inasmuch that the goal to be reached is stationary. But it, too, is an example of an “ Ignorantio elenehi,” there, being a diminishing series of unspent times, similar"'to the diminishing series in the previous ease of uncovered space or distance. The mathematical answer is that the sum of this series of diminishing times, namely, one half-minute, plus one-quarter, plus one-eighth, plus one-sixteenth, - plus etc. of a minute is one, which proves that the minute hand will reach its goal in one minute.

They are interesting questions to ponder . over, and possibly the reader may feel inclined to give further thought to them in the light of these explanations. It might be added that only recently the scientist Enstein defined “ space ” as a space in which “ time has been added to the three ordinary dimensions of length, breadth, aiid depth.” WEIGHING THE “TOTS.” The mothers of five tiny “ tots ” desired to weigh their babies, but the scales was a primitive one, and no weight lower than 101 b could be found; and though the oldest baby was 12 months old, others were younger, and likely to turn the scales at'less than 101 b. While discussing the difficulty the village schoolmaster came along, and, after weighing the little tots in pairs, an easy calculation enabled him to give each mother the correct .weight of her baby. The same pair were, of course, not weighed together more than once, and if the 10 weighings (each child with the other) were 161 b, 181 b, 191 b, 201 b, 211 b, 221 b, 231 b, 241 b, 261 b, and 271 b, can .the reader say what were the respective weights, calling the infants A, B, C, D, and S? WHEN A HUNDRED AND FIFTY. In the year 1937 the combined aged of “W.” and “ E.” will be exactly 100 years, when they will have been .married 25 years. ’ As children they went to school together,’ and in the year 1896 neither of the two was . yet in the “ teens,” “ W.” being then twice as old as “ E.” Two ■ years after they were married “D.” was born, and if in that year the mother was four-fifths the age of her husband, what will be the respective ages of the three, “ W. ” “ E.,” and “D.” when their years total 150? COMBINING THEIR POINT 3. . Each of three’ boy studen. had one of the opposite sex as a partner in a round of competitive events, but the sexes were no mixed in any of the contests, the partnerships being only in so far that, their points were combined. Let us call the three girls P O and I respectively, and their partners N T and S, and assume that out of a total of 36 points gained by the fair maids, P secured three more than O, and I. three more than P. Although N only gained the same number of points as his partner, and T only half the number that his associate' scored, rhe total gained by the three lads was much higher than the total of their partners, S obtaining twice as many as his colleague. Can the reader say who were partners, and what were the respective scores, if they all totalled 81?