INTELLECT SHARPENERS.

Otago Daily Times, Issue 20786, 3 August 1929, Page 23

INTELLECT SHARPENERS.

By T. L. Britok. A STUDY OF DIGITS. A study of digits, separately or in combination, and comparing the results arrived at when a given figure or number is submitted to the several processes of calculation in elementary mathematics, viz.: addition, subtraction, division, multiplication, square and cube roots, etc., etc:, provides an unlimited field of instructive amusement, and affords the opportunity of gleaming quite a lot of useful information by noting coincidences and peculiar characteristics of certain figures and numbers. Take the digit eight, for example, which when multiplied three times by itself produces five hundred and twelve (512); these three digits adding up the original eight. Can the reader find other examples of this kind in any number, say up to twenty-five! There are only two. ANOTHER ONE. Whilst on tins particular phase, here is another coincidence. Two numbers, two (2) and 47 (47) multiplied together give the same figures (reversed) as when both numbers are added together, viz.: ninety-four (94) and fortynine (49) respectively. A simple example is where both numbers are the same, viz.; nine (9), which multiplied by itself gives eighty-one (81) and when added gives eighteen (18). Now there is only one other example, of numbers under fifty, in which this -peculiarity exists, where their product together with their sum gives a total less than one hundred. .Can the reader find these two numbers? There arc only two or three examples altogether of this coincidence, but as in gome cases the numbers are fairly high ones the effort to find them would be somewhat laborious, hence this problem limiting the value of each of the two numbers to fifty, the total of their product and their sum being less than one hundred.

A TEA EPICURE. A gentleman having epicurean tastes regarding tea, invariably selects at the provision store the blend that is supplied to his house. On one ocasion the only grades in stock were priced at three shillings and fourpence, throe shillings, ,and two shillings and four pence per lb respectively, but the gentleman, well knowing the strength and flavours of these teas ordered a blend at three shillings and two pence per lb, of the three grades mentioned, giving an order £ or \ sib ‘ * s an €as y calculation to find how this order could be made -up, for there are several ways of mixing teas under these conditions, blit if. we stipulate that the least possible quantity of the most expensive tea was put in the mixture, it will make the calculation more interesting, and limit the problem to one solution only. How were the 151 b of tea made up with this added stipulation. girdling the globe. A correspondent (P. Nixon) had sent a query concerning the hypothetical question of placing a steel tape around the girth of the globe, and asks if the/problem which, by the way. is of stone-age origin, can be stated. Here it is, and those who are not aware of the solution will probably find it. difficult at first realise it. Let it be assumed that the, globe is a sphere whose circumference is 25,000 miles in length, and its surface_ regular and even. If a steel tape measuring twenty-five thousand miles be placed around its girth so that it just touches the globe everywhere, what would be the distance between the earths surface and the tape if the latter were increased in length by six feet, both ends of the tape just meeting as in the first case, and the distance be? tween it and the earth’s surface being the same all round? MOOREA TO PAAPARA. ~o n the road from Moorea to Paapara the village of Taravao is situated at the SO-mfie post from the former place. A tractor left the latter village on its way to Moorea at 8 o’clock in the mornmg, its, uniform speed throughout, with a road roller in tow, being at the rate of three miles in two hours. Jones, on a bicycle, left the same place at the same time, also bound for Moorea, and exactly two hours after starting he met a tramp walking to Taravao at an even rate of two and a-quartcr miles an hour. Later another cyclist, Brown, on his way from Paapara to Moorea, overtook the tractor f? , m , l^e3 rom the latter place and met the tramp exactly 40 minutes before reaching the 31-mile post. On the assumption that all four rates of travel were, maintained right through’ without stopping, can the reader say how far Brown was from Moorea when Jones arrived there?

LAST WEEK’S SOLUTIONS. THE ORIGINAL BLOCK. The area of the original square block was 169 square chains, the north and south triangular paddocks being 12 and 13 square chains respective!^ DISCOUNT FOR CASH. The actual cash paid for the balls was tJ 14s, the discount being 3 per cent, on the usual price. BALING OUT THE WATER. quantity of water was 3090 gallons, but as 9000 gallons were -nUT e s °akage accounted for 0910 gallons. tfWO BROTHERSMN VESTMENTS. The elder brother received £2600 and the younger £I4OO. TWO LINES CROSSING. Twelve (12) feet from the- ground, and this would bo the height with the ropes fixed as stated, no matter how far apart the posts are placed, 30 x °0 divided by 30 plus 20. The formula “is the product of the heights of the two posts divided by their sum. ANSWERS TO CORRESPONDENTS. Water Cistern.”—The problem stated that the holes were of equal size “ Bananas.”-— The point was that the word “fifth” was used advisedly in two senses, viz., “ a fifth part of one, and a “ fifth ” following a ' fourth. “ Intellect Sharpeners ” are not limited to mathematics. “ Excel.”—Will appear next week. R. Olson—Yes, there are other examples of which yours is one.