"NUTS !"

Evening Post, Volume CXIII, Issue 31, 6 February 1932, Page 5

"NUTS !"

I INTELLECT SHARPENERS j | All rights reserved. §

(By T. L. Briton.]

Headers 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 the "nuts" may appear harder than others, it will be found that none will require a sledge-hammer to crack them.

(By T. L. Briton.) ' SMALL CHANGE. / A shopkeeper whose business requires him. to have a good supply of small change on hand, keeps this in a drawer containing seven compartments, one for each denomination of New Zealand currency, from id to half a crown, seven in all. On a recent occasion, before putting fresh change into the till, there was the same number of coins in each of the seven compartments, and the reader will be able to find from the following particulars what sum was then in each of the seven parts of the till, as well as their number. Had there been one more coin in each of two of the "silver" compartments, the number of shillings represented in the total sum would be in the propor-' tion of nine to ten to the total number of coins. Without those extra two coins the amount of money in three of the compartments could be exactly changed for seven half-sovereigns, the sum in two of these receptacles being equal to that in the third; ' As one of these compartments held a sum equal to twenty-eigty shillings, there' should be no difficulty in answering the two questions asked. A FLAGSTAFF. On account of its elevation, 600 feet above sea-level, twelve wire stays are required to secure in a vertical position the mast at a signalling station...' The flagstaff is erected ,on a perfectly level piece of ground,, five chains square, two of-the wire stays that con-" cern this problem being made of rigid steel, both fixed to the extreme top of the mast, and the pegs in the ground which held these two stays were in direct line with the point at" which the mast entered the-, ground. • The two, pegs'in question are fortytwo yards distant- from.-one' another,and one of -the two stays is exactly forty yards long, while the other is shorter than that ■by as many feet as there are yards between the two pegs. .As the lengths of: the stays are the exact distances from the pegs- to the top of the pole, can the reader find the height of the mast and also the respective distances, from pegs to the bottom of the flagstaff? A PUZZLE IN £ s. d. Here is a ljttle curiosity in pounds shillings and pence which, should test the inventive skill of the would-be solver, for the solution cannot bo arrived at by any mathematical process known to the writer, methodical trials being the most interesting form of procedure. A sum. of money, less than forty .pounds, in ; which pounds, shillings, and pence are represented will, when multiplied by a digit not appearing in the sum referred to, give a result which can be expressed with digits not heretofore used. That is to say that in the wh.ol© operation ten digits, including the cipher, are employed, none, of which are repeated: Can the reader construct such a. sum and1 its answer? WITH "1" IN THE ONETEE. "Colenso" asks why it is that "13" is the only number that can occupy the central cell in a twenty-five magic square? The answer to this question is that the assertion is 'not correct, because any number from 1 to 25 can be used in the central space so that horizontally, perpendicularly, and diagonally, as

well as in other combinations, the numbers will add up "65." There is an arrangement of the numbers in such a,' square with "1" i a the centre which, if repeated'in ■nino-simi-lar squares adjoining any twenty-five cells in a group . selected at random from the two hundred and twenty-five cells, will form a magic square. ; Can the reader arrange the original square with "x" as the central figure which has these characteristics.? A "MEASURE" FROBELM. A correspondent, "Bex," has* sent a little problem concerning measures of capacity, but as it is one with ." the three, five, and eight quart vessels with which most readers are familiar, a puzzle. of the same kind but with a five, seven, and twelve quart measure will-be substituted. A man had a twelve-quart vessel full of sour milk, arid was about to-throw it away when a woman camo along for one: quarter of it, bringing with her a five-quart measure. . • . ' ; The man agreed to this, but did not see how one quart could bff exactly measured.into the five-quart vessel, the only other measure he had being; one of a seven-quaTt capacity. - ;; After fifteen pourings the woman obtained a quart of. the milk in her fivequart measure, and. the question is what is the least number, necessary with only these three vessels available, no tricks such as marking or tilting the vessels being allowed. A "pouring" may be on. the ground as well as from one vessel to another.