Intellect Sharpeners

New Zealand Herald, Volume LXX, Issue 21640, 4 November 1933, Page 5 (Supplement)

Intellect Sharpeners

BY T. L. BRITOX

ART UNION WINNER'S GIFT

A winner of the first prize in an art union distributed a certain sura amona eight institutions, A, B, C, D, K, I<\ 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, C. D, E, and F each receiving £2 10s. Half of the sum that was then remaining of the amount set apart for distribution in this way was given to G, nnc) fh<; balance to H. The two last-mentioned recipients secured similar amounts which together totalled £2O morfc than the combined sum given t<* A and B, the two latter receiving together 20 per cent of the amount distributed to the eight organisations. How much was donated? THREE FOR THE ARMOHAHt 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 the ceiling. .If the total cost of this was £1 lfjs, can the reader say without usinc pen or pencil how much per foot that cost would represent? A drainage work had been proceeding about a week when rain stopped further progress. If this happened after only 12J per cent of the money voted for the whole job had been expended, how much had been so voted if what remained was equivalent to a sum that wpuld produco £3 10s a month at 6 per cent per annum? Ten per cent of the " strength " of a corps of boy scouts were abtent from drill on a certain day, and of these 75 per cent failed to attend owing to having inensles. If 72 scouts attended, can the reader say, after reading the question once only, how many of tho absent ones could not claim measles as an excuse for non-attendance? CALCULATING HEART-BEATS

A correspondent, "Rex," is very keen to have an arithmetical puzzle which involves " plenty of figuring," as he describes it. Here is one that should fill these stipulations. How often does the heart beat in a life of 75 years of 36-5 days each, assuming that it beats according to the following record: During the first three years of life the number of beats is 140 to the minute, for the next three years 120 to the minute, 100 beats a minute during tho next six years, for the following 10 years 90 beats a minute, 75 during'the next 28 years, and 70 a minute for the following 20 years. If the pulsation then increases to 80 beats a minute and continues at this rate during the last five of the 75 years of life, what is the total number during the whole life? TEN DIFFERENT GRADES The quality of spirits contained in 10 jars of equal size in a merchant's cellar is different in every instance, apd if the vessels be labelled by the letters A, B, C, D, E, F, G, H, 1, 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 10 jars be arranged in two rows thus: * ABC D E FGH I J it will be seen tHut the spirits in a jar below another are inferior to that in the jar immediately above it, and also that the contents of any jar is 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 1 being the simplest. The question to answer, after making a simple calculation. fs in how many different ways can these jars 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 10 jars are to be formed in two rows of five jaw each. The number of different arrangements may surprise the reader when ho discovers it.

FILLING THE BLANKS Here is an amusing puzzle that will require a measure of skill and ingenuity to solve.* As will be seen by the diagram the five squares shows that 16 of the 25 cells are unoccupied b.v numbers, the other nine squares each containing a number of two figures. The. problem is to fill in a two-digit i number in each of the 16 unoccupied cells, so that (every small square then holding a two-digit 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. 17 - - - 24 f ■ - 32 - 46 - - - 14 - - - 19 - 16 - 22 - - - 20 LAST WEEK'S SOLUTION! Three Carpenters.—Jones 14J, Brown 174, and Smith 23 approximately. Three for the Armchair.—(l) 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 leapyears, two days aro to bo taken off when calculating with the _ jusunl formula, the day being therefore Saturday when Captain Cook first saw New Zealand on October 7, 1769. Alphabetical Sum.—The numerical equivalents, of the letters A, B. C, P, E, F, Ci, H, I, J are 6, 1, 7. 3, 8. 5, 0, 4, 9, 2 respectively. Thus tlw. quotient 15 in the last division is represented by tho sum of C and E. Art Uniofl 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.

Bad Motor-car Bargain.—This is an arithmetical progression in which the fifteenth term has the value 0, indicating that the car would come to a standstill one mile from its destination. ANSWERS TO CORRESPONDENTS " Curious ".—Problem and solution already published. A.B.C. —Thanks, but already published. y " Dominoes." —In the case mentioned the complete set should be used, otherwise no solution is possible. "Axiom."—lt is called a right pvramid when the axis is perpendicular to the base. When inclined to tho baso it is an oblique pyramid. || " Curious." —It is- obvious that must be «iu odd number of wiiicii means that there is a flaw'in your ... statement of the otherwiso ingenious .. . " X.Y.Z."— I The probabilities are 11to three against the yellow ' turning | up," but the game suggested would : much too intricate to be P°P ar those desiring mental re!axauon»^