NUTS TO CRACK.

Otago Witness, Issue 3882, 7 August 1928, Page 18

NUTS TO CRACK.

By

T. L Briton.

(For the Otago Witness.)

Reader* with a little Ingenuity will find in tis column an abundant store of entertainmei • and amusement, and the solving of the problems (should provide excellent mental exhilaration. While some of the "nuts" may appear harder than ethers. It will be found that none will require a sledge-hammer to crack them.

Solutions will appear in our next Icsue together with some fresh "auts."

t. Readers • re requested not to send In their solutions, unless these are specially asked for, but to keep them for comparison with those published in ths issue- following the publication of the problems. ELECTRIC DECORATIONS. When examining the electric decorations fo.. a recent function, the foreman found that ; n a row of ten blue and red lights over one of the entrances, the -clours ha.l been alternated blue, red, etc., instead of five reds being followed by five blue bulbs as specified. A workman standing on a platform, by taking a blue in one hand and a red in the other, quickly made the desired exchanges in three “ moves.” Here is a little problem on practically the same position with some conditions attached that will take some thinking to jolve. Let it be stipulated th A the bulbs had to be placed in their specified places, by taking them two at a time, each pair to be side oy side and kept so in their .iew positions irrespective of tneir colour. With these conditions and also the conditions t’ at the bulbs must be kept strictly in their order (left and right) throughout, what are the fewest number of “ exchanges” required to'place the five reds first and five blues following? At the end of the row of ten bulbs are two empty bulb sockets, which may be used when effecting the “ exchanges,” the empty ones to be left at the beginning of the row when finished—one “ exchange ” being the complete substitution of cne pair for another. Try th’s with counters, and it will be found a very entertaining puzzle. A SALE OF RAMS. A stock dealer attending a sale of Corriedale stud rams bought 48 of them at an average price < f £3l ss, and quitted •them ten days afterwards at the following figures:—Fourteen at 225 each, ten at £2B 2s 6d each, nine at«£4o each, and fifteen prize-winners • t’£s6 5s each. The dealer was working on another. man’s capital, the agreement betweeni them being that the latter was to provide the purchase money and receive 10 per cent, fo* the advance, all expenses* to be de-

frayed by the dealer. As the costs, including droving, paddocking, and food, amounted to exactly £5 less than the dealer’s net profits, what did he gain in th. venture ? NOT ON LEVEL TERMS. Two watermen A and B rowed a race. It was not to decide supremacy, for A was given a certain start, which, without stating exactly how much, was a distance it would take B 10 f his usual strokes to row over. A took four strokes to his adversary’s five, but, against that, six of B’s strokes were equal to five of A’s ,each rower maintaining his own rate of travelling uniformly throughout the race. With these figures as a guide can the reader say exactly how many strokes B must make before overtaking his opponent 1 When it is stated that six of B’s strokes were equal ‘to five of A’s it should be noted that “ equal ” mean s in time taken, not equal in distance. JOINING HIS MATE. A boy commenced a drawing of a new kind of radio cabinet, but had only completed a rectangle 30 inches by 18 with two .circles of equal size wholly within the figure one at each end of it, when he gave up the job. His drawing was according to specifications and geometrically correct. One end of the top side of the rectangle touched the outside circumference of each, circle, thus fc>’’ming a tangent in each instance. There were sever •! inches’ space between the bottom side of the oblong and the circumference of both circles. A few days afterwards, upon his entering _th e room, a snail was found hibernating on the drawing hoard at the exact centre of one of the circles, and another was lying at a spot within the other circle eight inches in a direct line to one of its tangents and nine inches from the other, also in a direct line. When the latter snail, upon being disturbed, moved to a point on the circumference nearest to the other circle, the situation immedidately suggested this question, viz.. How long would it take the snail to join his mate at the centre of the other circle if he proceeded in a direct line at the rate of an inch in 12 minutes? Can the reader say ? A BOARDING INSTITUTION. An institution which provides, in addition to its other services, board and lodging for apprentice boys, has usually a large number in residence, and a careful record is kept of the fluctuations in the cost per head as the number of boarders increases and falls. Let us assume then that 30 is the normal strepgth of those in residence, which may be taken as; the basis of calculations. If an addition of five boys increases the gross annual expenditure by £3OO, but diminishes- the 'average cost

per head by £l, can the reader determine, with only these figures to work upon, what the annual expenses are when - the number of boys in residence is at par—that is, at its normal figure of 30? Simple problems like this one are useful, and in that particular branch of the business they frequently arise.

LAST WEEK’S SOLUTIONS. FAMINE IN CHINA. Fifty thousand men, two hundred and fifty thousand women, tnd seven hundred thousand children total one million, were each supplied with wheat as follow’s:—l2 quarts per man, eight quarts per woman, and two quarts each child. PLANTING APPLE TREES. One hundred and twenty-five trees 20 feet apart can be planted on one acre of land in the shape of an equilateral triangle, and 109 when the land is in the form of a square, that is provided the planting can be done up to the actual boundaries. Dick’s “ apple ” cheque was thefore £8 more than Harry’s. A RAILWAY PROBLEM. The freight per ton should be £1 2s 8d for the given distance as set out in the problem. A FEAT. One readier informed the writer that it could be done in 19 moves, but upon being pointed out to her the lady agreed that she had overlooked one of the conditions. So far no correct solution has come to hand, but the offer made last week still stands. Here is the writer’s solution in 20 moves:— t.F.e.t.A.a.t.e.F.A.e.t.a.e.A.F,t,a,e,A, and that is probably the lowest possible number UNEQUAL SHARES. The grocer should receive £156, Jones £l2l Gs Bd, and the employee Hopkins £39. ANSWERS TO CORRESPONDENTS. “S. F.”r—Published- on May 8 last. (2) If you send it along it will be examined, but solution cannot be sent 1 before being published. “W. M. T.”—Thanks.

“ Defoe.”— lt you had a “ couple ” instead of the one castaway it would make the difference you state, but in solving a problem one must not go outside the limits of the statement of it. Taking things for granted has always been a bugbear to budding mathematicians.

“ T. P, D.”—Will appear with necessary adjustments next week.

“ J-. B.”—On the contrary it is the negative proof that is required. For instance, because we know from scientific

observation that the sun actually moves, it is not reasonable to assume that it has done so since the beginning of things? And similarly with regard to all natural elements.