Intellect Sharpeners.

New Zealand Herald, Volume LXVIII, Issue 20922, 11 July 1931, Page 5 (Supplement)

Intellect Sharpeners.

WITHOUT PAWNS.® , BI T, I<. BRITON. " ? The reader who does not play ches3 .<• need not pass this little problem for ' } that reason, for if he merely knows how the board is set up np skill or knowledge of the ph:y is needed. The board consists of 64 squares, eight by eighty 32 pieces being used, 16 for each To simplify the problem, the pawns be removed, leaving eight pieces on each'cside, namely a king, a queen, two bishops, two knights and two rooks, 16 in - all, each occupying one of the 64 squares, eight being on the outer line of the board, the remainder being in a similar position on the opposite side. The question is in how many different ways can the board be correctly set up with the 16 pieces ? The arithmetic of this is very simple, but it is quite possible. <. ( that an incorrect answer will result, oven; from chess devotees, for thsre is a little point to be observed which may trip the unwary.

A TEST OF SKILL. It will possibly test the ingenuity of the would-be solver to find the correct translation of the following jumble of words, none of which, as. written, are to be found in any dictionary of the language. All the letters employed, however, are those forming the original words, with the addition, in sundry, places of a few " redundants "; and the two sentences from, which the crytograph is are good plain English. Ife should be noted that a proper division into words has not been observed, and punctuation has been ignored except the full stops, the first being after the; word XPJYQRC. JEH TEREMTZ CAFFOX JAEGASSQXJEMG NIX EB DELAX JEG NOCROZ YLT JERCESQDEY JEVNOQ.C SEZ JOD TONX YIIX RAS SEC JENE KAMTIX ZAHQ- ' JPAR GOTZ XPJYQRC. ROFECX NATSNIS ZEG ASSEM NETTIRWN OZEHJI REPAPX ZGNIP PARWF JOSETZ TERAG JICROYBEH JTES QUFOK NIHC JIHWZ" SEMOX CEBELB JIS IVYJL NORE JTFAG NIEBJYL REXP JORP DETAZ ERTER JAYLTZ SOMNET TIXRWQ nini jalpeg a QUGN AZL.

A BENZINE TANK. A large tank in an oil-store had been filled with benzine to its full capacity, but by leakage it lost in 20 days exactly seven one-hundredths of its contents. This leakage was noticed and measured by an attendant, wKen he went to complete a sale of 301 gallons, which quan-. tity he then, drew off, leaving the tank exactly half full. An interesting question is suggested by these few particulars, namely, if the whole capacity of the oilstore is 91600 gallons, can the reader find by a very simple arithmetical process, how many tanks of the size of the one described could be filled . 1 £ benzine from the quantity that could ba stored in the shed when it is full to, its maximum capacity ? 1 hough this question is one which is possible to be correctly answered without resource to pen or pencil, yet is quite possible that the would-be solver will be tripped unless, he reads the statement carefully.

A CURIOUS FORMULA. There " is a curious formula in elementary arithmetic, which enables anyone knowing it .to. correctly determine any number sercetly written down, by,, another person and known to him only, by merely asking a. few indirect ques-. tions concerning it, v?hich can factorily answered by " yes "or no, neither the questions nor the answers giv-. ing any inkling to anyone not knowing the formula. To get, the niost fun out ;^vof this curious puzzle, the number selected should be a small one, say under; one hundred, so that it may be deajt t with mentally without effort, and rendering pen or pencil unnecessary. Sup- , posing for example the number written down is 50, the person demonstrating the formula will ask of the holder of the secret number six questions, one after. • another, and all precisely the the answers, '-'yes" or " no" being sufficient for the performer to immediately declare what the actual number is. Does the reader know how simply this can be done?

IN ROWS AND COLUMNS. Hero is an interesting puzzle with counters that should give the reader, perhaps half an hour of intellectual amusement-, particularly if he i adopts " trial " methods to achieve the object. Make a 16 square, numbering the cells 1 to 16, reading from left to right horizontally, starting at the top lefthand corner, and try to discover in how,, many different ways four counters can be placed, one in a cell, so that 'there will'not be more than one of them m the same row or column. Placing them diagonally is one way, but although there are two diagonals, it will be really only, one way that that position may count, neither will a reversal in any other manner, nor a reflection of a position cbunt as a different way. It may surprise the reader to know that there are only a few arrangements under these stipulations, fewer than one doj&en, and if the reader will spend a little time in discovering all of them, the timo should' pass quickly and enjoyably. LAST SOLUTIONS. Novel Competition.—'Twenty-three and a-half days, but if the distance had been in a straight line the shortest time possible would be 86. What is the Cost?—lf an article is marked for sale at thirty-three and a-third per cent, upon cost price, and sold at a reduction of- ten per cent, on the latter price, the profit would be 20 per cent., not twenty-three and a-half as several renders have written to say. The cost of the article in question was,, therefore, 10s.

Three Lengths of Roads.— I Twelve and a-half, ten, and seven and a-half, respectively. Five Orphans.—Ten . and a-half, fivo and a-quartor, three and a-half and on® and three-quarters. Equal Fines. —Two pence decimal two four. < • ANSWERS TO CORRESPONDENTS. "Calculus." —(1) Ratio can exist only. ; between quantities of the same kind, and there cannot be a ratio between fno minutes and three pence, or between three pounds and five quarts _ (2) MUic • - and water are of the same kind, viz., fluids. (3) Any side of a triangle may. be called its baso. "Wager."—A dealer's finances do not i remain in '-statu quo if he fi u y s , ~ articles at the rate of seven for five shniinKS, and sells 15 at the rate of three ; for two shillings, and 15 at the rate of j four for three shillings, though superfi- . cially ift may appear so. . You are these-. ; fore both wrong, bnt neither lopca.