"NUTS!"

Evening Post, Volume CXV, Issue 123, 27 May 1933, Page 22

"NUTS!"

INTELLECT SHARPENERS All rights reserved.

(By T. L. Briton.)

Readers with a little ingenuity will find in this column an abundant store of entertainment and amusement, and the solving of tho 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.

BY DEDUCTIVE REASONING.

A little pationco together with soino ingenuity, should enable the reader to reconstruct the following little arithmetical sum in long division from which a number of digits have purposely been erased. There are exactly thirty-four figures in the sum and working, including the repeated figures brought down in process of completion, but tho cipher does not appear in any part, and two of the nine digits are each represented once only throughout. Tho divisor wheu properly reconstructed has three figures, the first and last being missing, the remaining digit being a "two." There should be six figures in tho dividend, four of them being deleted,, tho third and last digits reading from the left being a "six" and a "nine" respectively. From tho quotient of four figures the two end oues are missing, tho others being n "seven" and a "one" respectively, reading from the left. The sum divides without remainder, and if it be stated that a "six" appears four times in the working, not including "brought dowu" figures, namely, in the "tens" place of each of tho first, second, and fourth multiplication, lives, and in the third lino of subtraction, tho reader will havo ample data to find the only solution of this intellect-sharpening puzzle. A QUESTION OF SALARY. At March 31, 1933, "XV bank account showed a credit balance of exactly one hundred and' seventy pounds (£170), his monthly salary being the only money paid into it, the account also showing the total expendituro under all heads disbursed by "X." Let' us assume for the purposes of a little arithmetical calculation that the account was opened on October ,1, 1931, the first payments to credit being, that month's salary. During the period between tho two dates mentioned, insurance, interest on mortgage, together with rates and taxes, represented twosevenths of "X's" annual income, ninefourteenths of which was ; absorbed by household expenses in the samo time, while one-sixth of it covered the exact amount represented ■by personal and unforeseen expenses for the period mentioned. When tho reader is finding what "X's" annual salary was at this time, it is suggested that tho question be ' read carefully before proceeding, otherwise he may bo caught, for it muy bo found not the "plain-sailing" puzzle that it seems at first glance. CUTTING AND FOLDING. Here is one for tho. armchair. An apprentice dressmaker was given the job one morning of cutting four rolls of muslin into lengths of two yards each, tho rolls being identical in every way, tho total quantity of muslin in the whole lot being two hundred and forty yards.: This work being completed, the girl was given the job of folding each piece cut, commencing tho latter work immediately the cutting was... finished, there being no perceptible delay. It took the same time "exactly to fold a length as to make- a cut (half a minute^ and the puzzle is to find how long the two jobs took tho apprentice to complete and the exact time that she finished the work if a start was made at 8 o'clock in the morning. And haying, found this, the question, that is prompted bythe incident is if two girls were employed to do this work, one to out while tho other folded, the former being paid at the rate of threepence per dozen cuts, and the latter at the rate of twopence halfpenny per dozen foldings, how much more would one girl get for her.work than the other A COLLEGE CLASS. In a senior class at a secondary school one-half of tho number of students received in a recent examination maximum marks in each of the subjects taken, namely, English, French, and Greek, Arithmetic, Algebra, and Geometry. The other half of the class took the same papers, but with varying success, none getting more than GO per cent, in any individual subject, their aggregate marks ' being only twosevenths of the total points gained by the whole class. The number of marks obtained by the more successful half of the class in the whole six eub.,^ jects,' there being an equal number of marks in each subject, was nine hundred, and if tho maximum number of marks for a subject is equal to three times the number of students in the whole class, how many were there if the whole of them were candidates at the examination in question? It was ; not intended when framing this littlo puzzle to make it one for the armchair, but it has been simplified in the process of preparation, so that the answer

may bo readily found without the aid of either pen or pencil. There is, however, a little pitfall ii; the statement which may catch the unwary..1 . A CRYPTOGRAPH. Here is an easy typo of cryptograph based on tho method adopted by Julius Caesar and also his relative Augustus, though neither used it in connection | with military exploits, reserving this [ method of disguise for private aud secj ret memoranda in their own establishments. The method of construction is so simple that it probably was not even in those days, safe to use the code in matters of extreme importance. Another form used by Julius was to move every letter of the original four places forward, writing "d" for "a," "c" for "b,". etc., but such methods would hardly be much, good in modern times, though possibly effective then. Although tho code now given is not based upon the latter-mentioned plan, its key should be quite as easily found, for tho would-be solver will no doubt quickly find that there is a similarity in many of the code words that should enable the code to be rapidly translated into intelligible English. Still, it is possible to get fifteen minutes of intellectual enjoyment unravelling the niesFXEMJNY GXXDRKJSXNS THKCXNSTEZCTQXN XFMQLQTJRY CXDKMKSSJGKS MZSTBK SXSQMPLK THJTTHKY CJNBK KJSQLY KNCQPHKRKD JNDDKCXDKD BYSPKCQJJQSTS LAST WEEK'S SOLUTIONS. Two Simple Questions. ' (1) 36 per cent, waste; (2) there were seventy-five. . ■ A Market Garden. As tho area must have .been onequarter of an acre, £.10 was received for one crop and £5 for the other. The "Hundred" Puzzle. There is only one example with one dio-it as the whole number, namely, 3 and OD2SS upon 714, resolving itself into 3 ; multiplcd by 1, to which 97 is added. Averages. (1) The daily expenditure was thirtythree shillings. (2) Subscriber, No. 6 must havo given twelve shillings to the fund, which made tho average for the lot £2 12s. , . ' • A Simple Cryptograph. The text is:—-''lt was .clear to observers that this calculating prodigy, only ten years of age, operated by certain rules, moving his lips as if expressing the process in words." Method: First write the sentence in code, beginning with the last word, "It was", after which the division into j proper words will be obvious.