INTELLECT SHARPENERS

Otago Daily Times, Issue 22023, 4 August 1933, Page 5

INTELLECT SHARPENERS

Written lor the Otago Daily Time* By T. L. Briton. A GAME Off CRIBBAGE. Three men, X, Y, and Z, aat down to play a three-cornered game of cribbage,---that is, each man played for himself, and there was a small financial interest on the result decided by points. The only money involved in the game was first placed upon the table, the total sum in 15 coins being twelve shillings, all in New Zealand silver currency. Curiously enough, each man had the same number of coins. X had the largest sum and Z the smallest, the latter having as much less than Y as X had more than the last-named player. The result of the game as determined by the respective points gained and lost, was that Z won sixpense from X, and also sixpence from Y. The first-mentioned two men settled their accounts by each exchanging two coins with the other, while Z and Y squared their differences by each exchaning one coin. The men then possessed their original number of coins,_ X having the same sum as Y started with, and / a similar amount to that held by X at the commencement of the with coins of two denominations only, and Y and Z with coins of three denominations each, what sum did they then have respectively, and how was each amount made up? This little puzzle is one for the armchair, for the reader will readily see that some of the details given are not essential, being included for intellectsharpening purposes. AGISTMENT OF COWS. A farmer had a large paddock which he used for the agistment of dairy cows belonging to a neighbour. The paddock had been “ spelled ” for several days immediately before twenty-nine cows were taken in. They consumed the, whole of the grass in exactly seven days. It eo happened that in the same month in the previous year under conditions _ exactly the same, both as regards the time and period for which the paddock had been “ spelled," and also as to the eating capacity of the animals, twenty-five cows conBurned the whole of the grass in nine days, the pasture in both instances growing uniformly. A few days after the twentynine cows had been removed from the paddock, during which time the block had been “spelled," another herd was placed there on agistment, and they ate the whole of the grass in six days, there being, as in the first instance referred to, a few days’ growth at the time the cattle were placed in the paddock, and as already stated there was always a uniform growth of grass on the section. If the price per head charged by' the farmer for grazing cows was threepence per day, how much should he receive for the agistment of the cows put on the area on the last occasion when they consumed the whole of the grass in six days, the conditions being precisely the same in other respects as m the two previous cases? TWO FOR THE ARMCHAIR. If a mao has £450 left of his annual salary, after paying his yearly insurance premium and .Government taxation, both payments being equivalent to 2s in the pound of his salary, how much does he pay in insurance premiums if the sum is in the ration of one to four to the amount paid in taxation, and what is his annual salary? . , A lady purchasing eggs at a shop •was told by the storekeeper that the Price was threepence per dozen higher it the customer picked the eggs from the box herself. She accepted the terms of purchase and personally selected a certain quantity for which she paid 3s 6d at the higher rate mentioned, lint had she been willing to let the seller , take the eggs at random from the box, the lady would have received three more eggs for the money she had paid. Can the reader say without using a pen or pencu. how many eggs did she get for her 3s 6d. PURCHASING GOLD DUST. A cold buyer purchasing gold dust from an assayer had the choice of three grades, none of which was the pure metal, the respective prices of the stuff being os per dwt for grade F, 4s 6d for grade G, and 3s 6d for the lowest grade of the three. The buyer, however, required first of ali a grade that could be certified by the assayer as a mixture of the three kinds at 4s 9d per dwt, based upon the prices mentioned, the quantity required being 20dwt. At first the assayer was in a dilemma whether this could be done, but after making a little calculation and finding that it was possible to do it in several ways he agreed to tiuhl the gold buyer’s order. Being a business man be selected the method of satisfying the request' that would be most advantageous to himself, and still conform f the terms of the order. This he did by making up the required parcel with the smallest possible quantity of the best grade dust, and it is for the reader to discover how the 20dwt were made up SO that the correct price of the three grades mixed together would be 4s 9d per dwt. SOLVING LOGICALLY. Here is a little question in alphabetical arithmetic that should interest the reader who prefers puzzles that are soluble logically, for in this case the solution may also be arrived at by the alternative and laborious method of trial and error, the latter process affording the would-be solver an opportunity of exercising his ingenuity. The problem is in the form ot a long division sum in which 10 different letters are used, each of winch represents a digit, the cipher included. The letters ] and 0 have been excluded in . that they may not be confused with the figures 1 and 0 respectively. JKL)MN L P Q ( R S MEKQ • .P T P~Q • PTPQ

A time, limit of 10 minutes should be suitable for the construction of this little sum arithmetically—by logical deduction, of course. ■ ■ SOLUTIONS OF LAST WEEK’S PROBLEMS. A "RESTORATION” SUM. Divisor 1111. dividend 11108880 and the quotient 9 9 9 9. TWO FOR THE ARMCHAIR. Forty-nine and 56. (2) There would be 81 posts required. TRANSFERRING CREDITS. £l2O, £IOO, £BO, and £6O respectively, each account having £9O to its credit at the end of the day. AN OLD QUESTION. The method by which this can be done is by ignoring the stipulation indicated by the word "direct" and passing one of the pipes through the house of a neighbour to its proper destination. ALPHABETICAL ADDITION. 395 6 7 - 24 8 7 043 1 0 106 3 6 4 The alphabetical total is A L M R M O, not A L A R M 0. ANSWERS TO CORRESPONDENTS. “ Alphabetical.”—Alternative methods could be adopted, but the results cannot vary. C. K. G.—lt is calculated that the sun s light travels the 98 million miles to the earth in eight minutes —approximately, of course. “En Zed.” —It is a good point, and opens up a new idea of treating the question, but the trouble is that, not being mathematical, it may lead one astray if followed blindly. “ Curious." —Another glance at the question is suggested. R. E. S. —Sorry, but problem sent is one by the Rev. E. F. 0., entitled “ The Solitary Seven.” “Mark.” —A capital budget. Thanks; this month.