INTELLECT SHARPENERS

Otago Daily Times, Issue 22101, 3 November 1933, Page 3

INTELLECT SHARPENERS

Written for the Otago Daily Times. By T. L. Bbiton. LIBERAL DONATIONS. A recent' winner of the first prize in one of the authorised art unions made some very liberal donations .to many deserving organisations, and an interesting as well as useful arithmetical puzzle can be made from the incident without the use of the actual figures or the names of the recipients. Let it be assumed that he gave a certain sum amongst eight institutions, A, B, C, D, E, F, G, and H, all in an even number of pounds. To A he gave 10 per cent, of the total amount, and to B one-ninth of what was left; the four organisations C, D, E, and F each received 50s. Half of the sum that was then remaining of the amount set apart for distribution in this way was given to Gy and the balance handed to H, It so happened that the two last-mentioned recipients secured similar amounts which together totalled £2O more than the combined sum given to A and B, the two latter receiving together 20 per cent, of the amount distributed to the eight organisations. How much was given? THREE FOR THE ARMCHAIR. A rectangular room has a superficial area of 18 square yards, its length being exactly double its breadth. A brass picture rail was placed around the room on all four Walls, parallel of course with the .floor and ceiling. If the total cost of this was 36s can the reader say without using pen or-pencil how much per foot that cost would represent? A drainage work had only been commenced about a week when heavy rain stopped all further progress. If this happened after only 12J per cent, of the money voted by the Drainage Board for the whole job had been expended, how much had been so voted if what remained was equivalent to a sum that would produce £3 10s per month at 6 per cent, per annum? , Ten per cent, of the “ strength ” of a corps of Boy Scouts, was absent from drill on a certain day, a'nd of this number 75 per cent, failed to attend owing to having measles. If the number of Scouts , who did attend drill that day was 72, can the reader say as soon as he has read the question once only how many of the absent ones could not claim measles as an excuse for non-attendance? I 1 CALCULATING HEART-BEATS. A correspondent, TRex,” is very keen to have an arithmetical puzzle which involves “plenty of figuring” as he describes it, though he confesses that, having left school a long time, anything beyond Standard VI work would now be too much of a strain. Well, here is one that should fill these stipulations. How often does the heart beat in a life of 75 years of 365 days each, on the assumption that, it beats according to the following record:—Duri ing the first three years of life the numI ber of beats is 140 to the minute, for the 1 next three years 120 to the minute, during the next six years 100 beats per minute, for the following 10 years 90 beats per minute, during the next 28 years 75, and for the following 20 years 70 per minute, j If the pulsation then increases to 80 beats j per minute and continues at this rate : during the last five of the 75 years, of life, what is the total number during the whole course of a life of three-quarters of a century? TEN DIFFERENT GRADES. The quality of spirits contained in ten jars of equal size in a merchant’s cellar is different in every instance, and if the vessels be labelled by the letters A, B, C, D, E, F, G, H, I, and J respectively, the quality decreases as the letters proceed | alphabetically. Thus the highest grade spirit is in jar A, and the most inferior in jar J, all the others being of graduating quality in the manner indicated. If the ten jars be arranged in two rows thus: — - \ _ _ ABODE FGH I J it will be seen that the spirits in a jar below anbther are inferior to those in the jar immediately, above it, and also that the contents of any jar are of a higher grade than the spirits in the jar of its right-hand neighbour. There are a number of different arrangements under these conditions, the one given being the simplest, and the question for the reader, to answer, after making a simple calculation, is in how many different ways these jars can be arranged so that the inferior grade is always in a jar on the immediate right of another, and also immediately below one of superior quality. Of course, the 1 ten jars are to be formed in two rows of five jars in each, and the number, of different arrangements may surprise the reader when he discovers it. FILLING THE BLANKS. Here is an amusing puzzle, the solution of which will require quite a measure of skill and ingenuity. As will be seen by the diagram,, the five square.shows that 16 of the 25 cells are unoccupied by numbers, the other nine, squares each containing & number of two figures. The problem is to fill in a two-digit number in each of the 16 unoccupied cells, so that (every small square then holding a twodigit number) each of the horizontal rows will add up 143. The cipher may be deemed a digit for this purpose, but no number must be used more than once. There is no condition requiring the numbers to be in any sequence, the reader 'having the choice of numbers 10 to 99, excepting the nine already shown in the diagram j !7 22 SOLUTIONS OF LAST WEEK’S PROBLEMS. THREE CARPENTERS. ' Jones 14 i. Brown 17J, and Smith 23 approximately. THREE FOR THE ARMCHAIR. (1) Two and a-half per cent. (2) 15s. (3) 35 runs in the fourth innings. ARRIVAL OF CAPTAIN COOK. As the years 1800 and 1900 were not leap years, two days are to be taken off ivhen calculating with the usual formula, the day being therefore Tuesday when Captain Cook first saw New Zealand on 7/10/1769. AN ALPHABETICAL SUM. The numerical equivalents of the letters A, B, C. D. E. F. G, H. I. J. are 61, 7 3,8, 5,0, 4,9, 2 respectively. Thus the quotient 15 in the last division is represented by the sum of C and E. AN ART UNION ALLOCATION. Hospital “A” is in the same town as Unemployment Committee “ Y,” hospital “ B ” and committee “ X ” being also in one town, as is also the case of hospital “C” and Unemployment Committee !Z.” , ANSWERS TO CORRESPONDENTS. “ Dominoes.” —In the case mentioned the complete set should be used; otherwise no solution is possible. X Y Z.”—The probabilities are fourteen to three against the yellow “ turning up,” but the game suggested would be much too intricate to be popular with those desiring mental relaxation, j “ Curious.” —It appeared on October 6, and the solution with an explanation of the method the following week.