Intellect Sharpeners.

New Zealand Herald, Volume LXVIII, Issue 20958, 22 August 1931, Page 5 (Supplement)

Intellect Sharpeners.

ALPHABETICAL SUM.

BY T. L. BEITON.

Here is a 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 " YZ" taken from " WX," the above statement making it obvious that the result of the last-men-tioned calculation is the same as UV." As each of the nine digits are employed and each represents the same letter throughout, can the reader make the necessary substitutions so that mathematically the sum stated alphabetically is correct? PECULIAR NUMBER. " J.O.S. " has sent' details of some peculiar features of a certain number which 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 bo multiplied by ony 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 tho digit selected at random 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 ft 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. They had not decided upon the length of their stay, so one of the party, more mathematical than the others, suggested that no two of them should occupy a table together more than 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 that supposing the first meal taken by the party was breakfast on Monday morning, and that everyone had three meals each day afterward, until each had dined with tho other at the same table the number of times specified, on what day and after which meal, did the visit end ? In . using the word " dined " it is not intended as a "catch," and it may be assumed to cover breakfast, " tiffin " and dinner each day. TESTING TWO CANDLES. Two new candles are placed upon the table and lighted v 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 of one j and a. half inches diameter and the smaller one with a diameter of exactly two-thirds of that. Under the conditions in which the test was made, the larger taper was guaranteed to burn for nine hours, while 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 t»vo 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 unburned length exactly one and a fifth times as long as the remaining part of the other ?

QUESTION OP AREA. The northern boundary of a block of land, oblong in shape, is forty chains in length, its eastern end terminating afc a watercourse which runs in a southeasterly direction, its banks also following that line. The south boundary is twenty-five chains from the northern, and the triangular section between the river and the rectangular block in question belongs to another party living across the river, who desires to sell it to the opposite landowner, 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 forty acres in area, the blockowner 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 an acre for it, but if less than that size he was to get it-at the rate of £ls an acre. As a sale was made under these conditions,' what did the farmer pay for the section ?

LAST WEEK'S SOLUTIONS. Pennies in Baskets.—Forty-eight married ladies and 16 single. ' Cryptographs and Ciphers.—Substitute the vowels A E I 0 U for the letters QVW X Z respectively. Read backward and then- divide into words. Thus the code RXHSVHT would be first ROHSEHT RET—then THESHOR TER —THE SHORTER. Perry and Cider. —Brown 15 and 17, Jones 19, 22, 23. Field o! Lucerne.—Three and threefifth acres. The Same Field.—As two acres would have been cut round the boundaries, it would be one-fifth more than what was left. Magic Ol a Figure.—Take the numbers 50 and 60 to be multiplied. Divide first by two and multiply second by two, ignoring remainder —. . •25 120 " Strike out multiplied \ 12 -0 numbers opposite even I 6 numbers in division o column and add. .. < 1 __j_ Equals .-. ... •• •• -• * 3000 ANSWERS TO CORRESPONDENTS. " Inquirer."—Although India is a silverstandard country the rupee has a fixed value to the pound sterling by Act ol Parliament, namely, 15« A.C.—The book will contain answers, as well as rules and formulae. T.H.F.—Thanks; both good. C.V.M. —Name listed. - "Bank-" —Thanks* '