INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVI, Issue 20324, 3 August 1929, Page 5 (Supplement)

INTELLECT SHARPENERS.

BY T. L. BBITON.

A STUDY OF DIGITS.

A study of digits, separately or in combination, and comparing the results arrived at when a given figure or numbei is submitted to tho several processes of calculation m elemeutary niatneinatics, viz: auciition, subtraction, division, multiplication, square and cubo roots, etc. etc., provides an unlimited field of instructive amusement, and aiiorus tho opportunity of gteaning much useiul inlormaiion by noting coincidences and peculiar characteristic of certain figures and numbers. Take tho digit eight for exampio which wnen multiplied three times by itself produces 512; tliesc three digits adding up the original eight. Can tlie reader lind other examples of this kind in any number say up to 25 ? There are only two. ANOTHER ONE. While on this particular phase, here is another coincidenco where two numbers, viz. two and 47 multiplied together givo the sa,u.e figures (revcised) as whon both numbers are added together, viz: 94 and 49 respectively. A simple example is where both uumbers are the same, viz. nine, which multiplied by itself gives 01, and 18 when added. Now there is only one other example of numbers under 50 in which this peculiarity exists, where their product together with their sum givo a total less than ICO. Can tho reader find these two numbers ? There are only two or three examples altogether of this coincidence, but as in some cases the numbers are fairly high tho effort to find them would be somewhat laborious, hence this problem limiting the value of each of tho two numbers to 50, tho total of their product and the sum being, as stated, less than 100. A TEA EPICURE. A man having epicurean tastes regarding tea, invariably selects at the provision store, the blend that is supplied to his house. On one occasion the only grades in stock were priced at 3s 4d, 3s and 2s 4cl per lb. respectively, but tho a;u well-knowing the strength and flavours of these teas ordered a blend at 3s 2d per lb., of tho three grades mentioned, giving an order for 151b, It is an easy calculation to find how this order could be made up, for there are several ways of mixing the teas under these conditions, but if we stipulate that the least possible quantity of the most exnensive tea was put in the mixture, it will make the calculation more interesting, and limit the p-oblem to one solution only. How wpre tho 151b. of tea made up with this added stipulation ? GIRDLING THE GLOBE. A correspondent has sent a query con- _ coining the old hypothetical question of placing a steel tape around tho girtli 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 tho solution will probably find it difficult at first glance, to realise it. Let it be assumed that the globe is a sphere whose circumference is 15,000 miles in length and that its surface is regular and even. If a steel tape measuring 25,003 miles be placed . around its girth so that it just touches tho globe everywhere, what would bo tho distance between the earth's 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 between it and the earth's surface being the same all round ? . MOOREA TO PAAPARA. On the road from Moorea to Paapara tho village of Taravao is situated at the 50 mile post from tho former place. A tractor left the latter village on its way to Moorea at eight o'clock in the morning, its uniform speed throughout, with a road roller in tow, being at the rato of threo miles in two hours. Jones, on a bicycle, left the same placo at the samo time also bound for Moorea, and, exactly two Hours after, ho met a tramp walking to Taravao at an even rate of two and a-qeava'r miles an hour. Later, another cyclist Brown, on his way from Paapara to Moorea, overtook the tractor 45 miles from the latter place and met the tramp exactly 40 minutes before reaching tho 31-mile post. Assuming 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 tho original square block was 163 square chains, the north and south triangular paddocks beinc; twelve and thirteen square chains respectively. Discount for Cash. Tho actual cash paid for the balls was £9 14s, the discount being 3 per cent, off the usual price. Baling Out the Water. Tho original quantity of water was 3090 gallons but as 9000 gallons were baled out the soaknge accounted for 5910 gallons. Two Brothers' Investments. The elder brother received £2600 and the younger £I4OO. Two Lines Crossing. Twelve (12) feet from tho ground, and this would bo tho height with tho ropes fixed as stated, no matter how far apart the posts are placed, 30 x 20 divided by 50 plus 20. The formula is tho product of tho heights' of tho two posts, divided by their sum. ANSWERS TO CORRESPONDENTS. Water Cistern.—The problem Stated that tho holes were of equal size. " Bananas." —The point was that tho word " tiftil " was used advisedly in two senses, viz. "a fifth part of one, and " tilth " following a fourth. Intellect Sharpeners" are not limited to mathematics. " Excel."—Will appear next week. E. Olson.—Yes, there are other examples, of whu'h yours is one.