INTELLECT SHARPENERS.

New Zealand Herald, Volume LXIV, Issue 19762, 8 October 1927, Page 5 (Supplement)

INTELLECT SHARPENERS.

BX T. L. BBITONv . m. Readers aro requested net to send in their solutions unless these are specially asked for, but t. keep them for comparison with those published on the Saturday following tho publication of the problems. AN ADDED AEEA. A square pie >e of suburban land belonging to a council was used as a children's play area, but its size, two chains squaie, was too small for the purpose. Municipal lands surrounding it were vacant, so ifc was decided to enlarge the area, and still retain its square form. Although the present ground had been fenced for some years, tho material was all sound and suitable for removing and re-erection. The four corner posts were practically as good as new, but being so tar in the ground and the earth so hard, it was decided to leave them for use as ordinary posts on the boundaries of the new block. The contractor was instructed accordingly, and to fence, in the form of a square, the, maximum area possible under these conditions to include, of course, the present section. Assuming that the whole of tho old fencing was used on the new boundaries, what additional length would be required to enclose the large square section, gateways, etc., being deemed "fencing" for this purpose. ANOTHEE TETHEEED ANIMAL. So much interest was shown in a previous problem concerning a tethered animal, that another one is now submitted. The present problem, however, is simpler and of more practical use, requiring & knowledge of elementary mensuration only - to solve it. The paddock is in the form of a right angled triangle, whose base and perpendicular are of equal length, and whose area is two acres. It is required to find the length of a line to which an animal is tethered on the other boundary of the paddock, that would enable it to graze on one quarter of the area only, assuming that the anima! can feed up to the end of the rope. It is understood that the area grazed upon must be wholly within the paddock, and not merely an area equal to one quarter the size of it A solution to the uearest half foot will be sufficient. SHARE MILKERS. A dairyman had two herds, exactly the same number of cows being in each, one compnsmg all Shorthorns, the other Polled Angus. Two men engaged to do the milking started one morning, one for W1 h l rd ' / oneS had milked five of one Kr W n e " reache <* the sheds, the latter proceeding at once to bale up a a„1Z S r a, !f Sh J rthor '' heite - AltSy an expert milker Brown was nervous with SET " 6j0 "» thi, pin.H i ""i 17 ?" ""I' 'ho mor, docile rolled Angus herd, which he did. With beine a f T® mi , ! j ked JonßS < and nHrflv milker, Brown finished qiackly and then went across to the ether shed, milking seven of the now quiet Shorthorns, which finished the morning s milking Who milked tho greatest number of cows and how many more than the other man? ~ ' ' FIVE ORPHANS, 01*? an "*|ry, 1926, Mary reached 1:« <Slst birthday being the eldest and oniv ? l -n jP a y fi ye » whose parents were killed in a motor-car accident a vear previously. If they had been alive when Mary came of age their combined ages would have been exactly double the united ages of the five children, and although the father was only fcnr years senior to the mother there " was a "time when he was twice her ag6. On Mary's* 21st birthday Jack was twice as old as Leon, Sam's and Leon's ages combined equalled twice Jack's age, and Dick's and Jack's ages together were twice the coxpbined ages of Leon and Sam. If the united ages of Mary, Sam and Leon equalled at that time twice the combined ages of Jack and Dick, what were the respective ages of th% four boys when Mary turned 21, and how old were the parents at their death ? A DEAL 13? FERTILISERS, A merchant had a pertain sum ol money,■which could not be exceeded, that had been earmarked for the purchase ol a quantity of super-phosphate at £8 a ton, and a similar quanitity of a cheaper fertiliser at £6 a ton, intending to mix them and retail at £lO a ton, which waj the ruling price of the mixture in equal proportions The manager of the fertiliser works, however, misread the instructions, and instead of consigning equal quantities to the amount of the available money, hs divided the money into two equal parts, and forwarded as much of each bind ol fertiliser as one half the money would purchase at the rates quoted, viz.", £8 and £6 a ton respectively, the same amount thus being expended on each. The two varieties, though ot unequal quantities, were mixed in the usual way, and the mixture sold at £lu a ton. If by so doing the merchant made a profit of £2O more than he would have realised had the consignment been in accordance with his instructions, what sum was invested in the two fertilisers ? LAST WEEK'S SOLUTIONS. Contradiction in Terms. The explanation published last week has probably left no doubt in the reader'* mind as to the existence or otherwise ol the number under, the conditions related. Four Waggons. The cost of the cheapest wagon waj £6, the others being £ls, £24, and £24 respectively. Husband and Spouse. The husband must- have bean 56 and his spouse 12 years of age at the time oj the conversation, and 28 years previously he would therefore have been twice bei age. Rectangles and Squares, 1. The length of the inner rectangle must be 285.3 units, and the angles 22deg. 18min. and 67deg. 42min. 2, From the point of intersection ,oj the diagonals, draw a line to on« of the sidys of the square parallel with its base. Then with the intersecting point mentioned as tne centre, arid th< line so drawn as a radius describe a cir. cle. The points where the circumference intersects the diagonals will be the foui corners of a square inside and concentri* with the larger one, and exactly one-hall its area. Financing a Gymnasium. The sum required to be raised wai £l5O, equally divided between 30 mei*. bera, the original membership being 20. ANSWERS TO COEEESPONDENTS. B.T.—The problem stated that fht launch travelled in a direct line betweer the two points, so it must be assumes that currents did not affect it laterally. i C.B.—Quite correct, the only pcssibli way, except by guesswork. , TW —A prismatic compass is not § substitute for a theodolite, though it u a useful instrument. E S M.-Th» mcidcnt <£?> - ■ " brain-clearer- • m a Pressed stamped envelope re i atd aa illustration of tha pom ceived, and an " condition! has been sent. Under j th( » a .T3 h j« original cow was j progeny would be 1.~