INTELLECT SHARPENERS

New Zealand Herald, Volume LXVI, Issue 20366, 21 September 1929, Page 5 (Supplement)

INTELLECT SHARPENERS

A DWARFED TREE,

BT T. L. BRITON

A treo standing by itself in a paddock reached its maximum height, viz., 36ft., long aftei othei similai trees planted at the same timo had attained greater stature. Tho tree reached 12ft. high seven years aftei being planted, and it was then given attention by more adequate protection and cultivation Let it bo assumed that when the, tree began again to grow from tho height of 12ft., it attained a certain increased stature at the end of the year following, and that in every year afterwards unt.l it readied tho maximum height stated, viz., 56ft., it increased uniformly in its upward growth by exactly two-thirds of the increase in the preceding year What height was it at the end of 12 month* from tho time it began to grow again at 12ft. high ?

A SQUARE SIX BY SIX.

Although this problem concerns a magic square the question involved does not follow tho usual form of requiring the respective 36 numbers to be arranged in tho orthodox magic fashion, but merely to ask the reader to discovet what digits and numbers should tho squaio contain under the following conditions:—Tho numbers aro not consecutive but run in arithmetical progression, the common difference between any ono number and tb» next, being three, and the point is that if, aftei 5b numbers have been arranged, the six rows, six vertical columns, aad tho two long diagonals each add up 367. What is the highest number in the square ?

ESTIMATING THE MILEAGE.

The question of the s»ileage of the unpegged road betweeu V aud Z was tho subject oi discussion between two members ol a trampers' club, both of whom had been ovei the road separately,' but never together. Hopkins. left Y on a certain date and the daily distanco travelled after the first day until ho reached Z was greatei than that oil the preceding day by the dame number of miles. The journey occupied fom days, and the return trip one day less, the daily increase, however, being the same as on the outward walk. Tompkins, on the other hand, walked the same distance every day. his daily record showing one milo more than Hopkins walked on his second day out, the former taking eight days for tho return trip. Both men followed the same route throughout, and tho reader will, no doubt, enjoy the fcffort to find the distance between Y and Z, for it involves a calculation just a little out of the ordinary character.

IMAGINARY AND OTHERWISE.

If a complete ljst of words—imaginary and otherwise—were compiled, so that every word in the compilation had a different pair of initial and ending letters, can the reader say how many words there should be in the full list ? For example a word could begin with P and end with Q, and vice-versa, 01 either letter could both commence and end tho same word, but tho same pair .'of letters must not occur in their respective positions in more than one word. It is immaterial what other letters make up a word, as the problem is confined to tho combination of the first an'd final letters. Although the calculation is an easy one, there is a short and very simple formula for it.

BAKER'S DOZEN AND THE OTHEE.

If wo take 13 matches of uniform size and form an oblong by placing three of them on each of the two longer sides, and one at each end, it is obvious that with the remaining five matches the figure can bo partitioned into six oblong compartments of equal size But if we Lad, just a bare 12 matches- instead of tha baker's dozei, can the reader discover a method of forming them into a figure which will also contain six compartments of equal size, using, of course, the whole of the 12 matches, none of which should bo cut oi bent ? The reader who is not aware ot the method of solving this useful little geometrical problem will find that it may afford him excellent mental exercise, foi there is only one way of demonstrating it under these conditions.

LAST WEEK'S SOLUTIONS.

Game of Fenny Poker.

Tho couples were: Y'6, A 12; X 9, B 9j and Z 30. C 15.

Minor Customs Receipts.

Tho receipts under. R for tho year ended March 31, 1928, were 50 per cent, more than those under M for that poriod, being in the proportion of 3 to 2.

A,Training Track.

Tho outer circumference being wholly within the square paddock of 625 acres, the diameter of the circle 18 20 chains, and as a ratio of 3 instead of 3.14159 to 1 was assumed, the outer circumference is 60 chains in length.

A Hard Bargain.

Tho sum of £36 being the interest on £IBO for four months at 60 pel cent., and tho goods costing the womarf £40 tj th# cash received by her was £lO4 only. J-h# dealer's profit was, therefore, £SO plus £36 —£66 representing a gain at the ratio of 110 per cent per annum on £IBO.

Weighed la Couples.

The respective weights are 106!b„ 1121b., 1161b., 1181b., and 1241b. As each of the five boys went to timet, there were ten weighings.

ANSWERS TO CORRESPONDENTS.

Probate.—Tho V usual practice" whatever it be, is not material. The point mentioned, however, is quite a good one. Obvious. —Your plus sign should obviously bo a multiplication one, and it is always safer to write the word in cases like this where the signs are somewhat similar.

Probabilities. —3 to 5, 7 to 6, and 4 to 7. Tho answer to your other question may be deducted from these results.