NUTS TO CRACK

Otago Witness, Issue 4038, 4 August 1931, Page 61

NUTS TO CRACK

By

T. L. Briton.

(For the Otago Witness.) Readers with a little Ingenuity will find tn this column an abundant store of entertainment and amusement, and the solving of the problems should provide excellent mental exhilaration. While some of th- ” nuts " may appear harder than others. It will be found that none will require a sledge-hammer to crack them. Solutions will appear tn our next Issue, together with some fresh ’’ nuts." Readers are requested not to send In their unless these are specially asked for. but to keep them for comparison with those published in I the Issue following the publication of the problems A SKELETON CODE. “ Skeleton ” cryptographs are usually not dnneult to unravel, except where a cipher ’ is introduced embodying arbitrary letters ' or ,'ymbols. In such cases the correct ' translations are often beyond experts in ' this kind of 'service. But' here is an ordinary one that may give the reader quite a lot of hard thinking before the i key is found, or rather before the words j are restored to their original form. Ex- i cept for the deleted letters, each of which is indicated by a dot. all words are as in I the original, an extract taken from a ! recent leading article upon a subject : known to everyone. In order that the : may not be too obvious, the , method adopted in dropping letters, is not ] a uniform one. A S..R.IT OF .0.15 .A. i BE .U.E. .U. AS A M.. 0. «F..TO. IN • THE ..E.T.ON OF THE .O.LD j .E.R.S.I.N (Stop) THE C.US. IS .0. ' THE .O.K.N. OF THE M..ET.R. S.S.EM | .U. THE .N.I.E A.C..U.A.1.N OF THE ■ .O.L.’S P.I.C.P.L .O.DS.U.FS .N. .A. I M.T..IA’. The reader will note that in j one or more instances the deleted letters do not dkguise the identity of the word. i LEFT ON THE PLATFORM. A large number of neople purchased | their tickets for a railway excursion on a recent holiday, and waited on the plat- i form for the carriages to be drawn up. ' Some of them, however, were left behind, j as the first division could not accommodate | all of them. The combined number of ' travellers that left by that train was ■ greater than the number who remained behind, the latter numbering nine more than those who travelled first class, while those with second, class tickets who managed to get away by that train numbered three times as many as those who travelled first class. Everyone, including the “ left behinds,” had adult tickets of one or other of the two classes mentioned, the cost of each being at the rate of 3d per mile for first, and 2d for second. All passengers, however, were not bound for the same destination, the tickets indicating that the distance to be travelled by the “ firsts ” averaged 120 miles, and by the others 50 miles. On the assumption that the total co.-t of all tickets held by the intending tourists was £390 Is Bd, and that those left on the platform were all second class passengers with the same average distance as I the others, can the reader say how many people travelled in the respective classes, and how many were left on the platform? MILK AND WATER. The profits made by adding water to pure milk and selling the mixture as the genuine article were exposed in a recent ease in the courts, and the details suggest a little problem. The milk vendor bought a quantity of pure milk from a dairy farm, and paid lid per gallon tor it. After adding water to it, he sold the mixture at the rate of 7Ad per quart. If the sales of the milk diluted in this way extended over a whole week in daily transactions, and the profits during that period showed 50 per cent, on the original cost of the pure milk when purchased by the retailer, can the reader find by a very simple calculation what proportion ot water was added to the pure milk? The figures given are not those of the actual case against the milkman, but are assumed for the purpose of formulating a more in- ■ teresting problem. The question which requires a correct answer is, What was the proportion of milk to water in the mixture? A CURIOUS DISTRIBUTION. A bag containing fewer than 25 dozen oranges was sent by the Fruitgrowers' Association for distribution amongst the children from the earthquake area. To find, from the details of the curious method of distribution, what number of oranges was in the bag when sent should afford the reader a useful calculation as well as providing material for interesting mental recreation. There were four groups of children participating. They may be called “A,” “ B,” “ C,” and “ D,” and the first act in the distribution was that of dividing the whole of the fruit by four and handing out to group “A” in equal allotments, om Quarter of the whole lot. When this division was made there was one orange over, which was shared by the four distributors. The remaining fruit was again divided by four, and again there was one orange over, which was dealt with as in the previous divis ; on, group “B” receiving in equal shares one-fourth of the lot, as -in the case of group “A.” Two more similar divisions and distributions were made in turn to group “ C ” and " D ” respectively, there being again one over in each division, which met a similar fate to the previous remaining ones. With these meagre details can the reader find how many oranges were in the bag before distribution if those in group “ D ” each received two? WHAT PAGE WAS IT? A few weeks ago a problem appeared in this column concerning the size of a book measured by its pages. Since then several communications have been received from readers, each submitting problems somewhat similar. Upon examination, however, only one was found to be suitable, the so’utions of the others 1 either being too obvious or the calculations too complicated for the average reader. Here is the selected one, which

is somewhat on the same lines as the one mentioned above, though the process of reaching the solution is different. A book lay on the table opened at a certain page, the number being an even one, and the problem is to discover what page the book was opened at, the only information that is available being as fol lows:—The book contains more than 400 pages, but fewer than twice that number, and the sum of the numbers of the pages from -one up to the open page referred to (both inclusive) is equal to one-half the sum of the numbers of all the pages in the book. At what page was the book open, the number as stated being an even one? RABBITS. The recent discussion in the Daily Times upon this debateable subject has one phase which more particularly interests this column—mainly, the extraordinary rate at which these rodents multiply, anj that point of the discussion affords excellent material for useful arithmetical study. I do not intend to go elaborately into the method of calculating results under the many varied conditions that may apply, but will give a simple illustration of the productiveness of a single pair under conditions as near as possible to those laid down by the two debaters. It is noted, however, that both correspondents omitted an essential point, iiamely, the age at which a young doe has her first Ift’er. But if we put this down at two months, which I am informed “ i- s .about it.” and adopt “ Sheet Anchops” estimate that a doe produces a litter every 21 days (say 20 for simpler cal-ulation), it will be found that if a pair of rabbits produce a pair on the first day of the breeding season (male and female), and continue producing a pair every 20 days thereafter for six calender m-mflis (10 litters, not nine), and the females of the progeny as they mature at two months produce similarly every 20 days until March 31 (on the assumption that the first litter was on the first Octob'r), the original pair would be ancestors in direct line of 178 rabbits (89 pairs) on the one hundred and eighth day or last day of the season. If, however, we base our calculation upon an average litter of 10 (five pairs), which one of the controversialists considers is a fair average, a land-owner with only a small stud of 100 pairs to start with, could, if he chose, muster at the end of six months a flock of nearly 150.000 of these prolific animals, provided, of course, that he was unlucky enough to have lost none.

SOLUTIONS OF LAST WEEK'S PROBLEMS. A CRYPTIC PARAGRAPH. The famous diary of Samuel Pepys is commonly said to have been written in cipher (written cypher), but in reality it is written in shorthand. It is, however, difficult to read, for the vowels are usually omitted, and Pepys used some arbitrary signs. The reader will note that most words have been coupled and letters written alternately thus: — Teaoshfinu—for “the famous." A CURIOUS DEAL. 58800—£16—Id. FOOTBALL ACCIDENTS. Seven. Two with a left arm injured, three with the right, and two with both. AT A RESTAURANT. Fourteen must have been absent at the week end. NO ALTERNATIVE. Twenty-four minutes to spare before noon. ANSWERS TO CORRESPONDENTS. “ C. C.” —A similar one appeared on April 21 last. Thanks. “Inquirer.”—(l) A train rounding a curve tends to move in a straight line, but is forced by the pressure of the rails to continue in the required direction. (2) The outer, not the inner, rail is where the pressure exists. Sorry both wrong.