NUTS TO CRACK

Otago Witness, Issue 4041, 25 August 1931, Page 65

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 thw " nuts " may appear harder than others. It will be fount! that none will require a sledge-hammer — to crack them. Solutions will appear in our next issue, together witli 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 AN ALPHABETICAL SUM. Here is a little curiosity in the form of a sum in simple arithmetic in which letters of the alphabet are used instead of digits, and if it does not give the reader a lot of hard thinking before the solution is arrived at it should at least afford material for the exercise of his ingenuity. Twice R equals S plus T, and when UV is subtracted from WX it will leave YZ. Again, if ST be multiplied by R it will give exactly the same result as Y’Z taken from WX, the above statement making it obvious that the result of the last-mentioned calculation is the same as UV. As each of the nine digits is employed and each represents the same letter throughout, can the reader make the necessary substitutions so that mathematically the sum stated alphabetically is correct?

A PECULIAR NUMBER. J. O. S. has sent details of some peculiar features of a certain number which it should be worth the reader’s while to investigate. The number consists of eight of the nine digits written in their proper order, and if this number be multiplied by any one of the digits comprised in it, and the result again multiplied by any one of those digits (selected by the person demonstrating the curiosity), the product will be a repetition of the digits selected at ran-

dom and made the first multiplier. Another curious feature of that number is that after obtaining the result of the calculations described, the sum of the repeated digit will be found to be the same as the product of the two digit multipliers, the one selected haphazard by one of the audience, and the other by the person submitting this peculiar number for investigation. Can the reader find the number?

TWO AT A TABLE. Six friends, staying at an hotel at a time when business was brisk, were unable to get a table for six people, but were given three smaller tables in a corner of the dining room, each table seating two. As they had not decided upon the length of their stay, one of the party more mathematical than the others suggested that no two of them should occupy a table together more than three times, and- as soon as each one of the six had sat at three meals at the same table with each of the other five, their sojourn at the hotel would automatically come to an end. This was agreed to and the interesting question for the reader to answer is this: Suppose that the first meal taken by the party was at breakfast on Monday morning, and that everyone had three meals each day afterwards until eaeh had dined with the other at the same table the rumber of times specified, on what day and after which meal did the visit end? The word “dined” is not intended as a catch, and may be assumed to cover breakfast, ‘ tiffin ” and dinner each day.

TESTING TWO CANDLES.' Two new candles are placed upon the table and lighted at precisely the same time, both burning under similar conditions until extinguished. Each candle is eight inches in length, but one is larger than the other, the former being of one inch and a-half diameter and the smaller one having a diameter of exactly twothirds of that. Under the cc iditions iu which the test was made, the larger taper was guaranteed to burn for nine hours, whilst the other one's time was in the

same ratio to nine hours as the smaller diameter is to the larger. They continued to burn under the normal conditions'* stated, but before the period of the small candle’s maximum time had expired both were extinguished together, and the respective lengths of the two remaining pieces were measured. Can the reader in a very simple calculation find how long the candles were allowed to burn, if upon measurement it was found that the larger of the two had an unburnt length exactly one and a-fifth times as long as the remaining part of the other?

A QUESTION OF AREA. The northern boundary of a block of land, oblong in # shape, is 40 chains in length. Its eastern end terminates at a watercourse which runs in a south-easterly direction, and its banks also follow that line. The south boundary is 25 chains from the northern, and the triangular section between the river and the rectangular block in question belongs to a person living across the river who desires to sell it to the opposite land owner, particularly as the latter's fence on the south boundary also terminates at the riverbank. It was all a matter of area, for, if the section was not at least 40 acres in area, the block owner stated that it was no good to him. It was thereupon agreed to have it measured, and if it were found to be of the area mentioned or more the purchaser would give £2l per acre for it, but if less than that size he was to get it at the rate of £l5 per acre. As a sale was made under these conditions, what did the farmer pay for the section ?

SOLUTIONS OF LAST WEEK'S PROBLEMS. INTO THEIR WORK BASKETS. Forty-eight married ladies and sixteen single. CRYPTOGRAPHS AND CIPHERS. Substitute the vowels A E I O U for the letters Q V W X Z respectively. Read backwards and 'then divide into words. Thus the code RXHSVHT would

be first ROHSEHT .”.ET, then THESHOR TER—THE SHORTER. PERRY AND CIDER. Brown 15 and 17, Jones 19, 22, and 23. A FIELD OF LUCERNE. Three and three-fifth acres. THE SAME FIELD. As two acres would have been cut round the boundaries, it would be onefifth more than what was left. THE MAGIC OF “TWO.” Take the numbers 50 and 60 to be multiplied. Divide first by 2 and multiply second by 2 —25 120. ignoring remainder; 12 240, *6 4SO, 3 960, 1 1920. Strike out multiplied numbers apposite even numbers in division column and add — equals 3000. ANSWERS TO CORRESPONDENTS. “Inquirer.”—Although India is a silverstandard country, the rupee has a fixed value to the pound sterling by Act of Parliament —namely, 15. “A C.” —The book will contain answers as wel as rules and formulae. “ Bank.”—Thanks. “ T. 11. F.” —Thanks; both good.