INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVII, Issue 20668, 13 September 1930, Page 5 (Supplement)

INTELLECT SHARPENERS.

ON THE BRIDGE.

BI T. L. BRITON.

A nautical correspondent, " Lousdalo Crescent," writes as follows" The following problem might prove of interest to your readers. I was on the bridge of the old Mararoa, and also tho Maori, for five and a-half years in the days when thoy left Wellington at 11 p.m., and provided weather conditions were not sever® we could always depend upon passing each other at practically the same timo every morning. The Maori steaming 19 knots an hour, leaves Wellington at eight o'clock at night, and the Mararoa leaves Lyttelton at six p.m. travelling At 14 knots an hour. At these uniform rates, at what timo should thoy pass one another?" With the consent of the correspondent this may be simplified by adding that the wind assists the packet bound south, and retards the other double that distanco which in the latter case is two knots an hour, a knot being deemed for, this purpose a standard of measurement*

PARALLEL TRAVELLING.

The direction that a steamer was travel ling along the coast and of a person walk* ing on the shore were parallel, thougK opposite. As the man walked, a per. pendicular flagpole on tha beach came in direct line between him and the extreme forward end of tho 6teamer, and continuing he kept both in the same line for the space of ono minute and a-half, daring which he had walked 64yds. At this point a second pole 300 yds. away, camo in lino both with the first one and the point on tho steamer described, the original flagpolo being then 200 yds. from him. He still continued walking, keeping pole No. 2 in line with the steamer's foremost end for another minute and a-half, during which time he travelled 100 yds., when he stopped. If at the precise moment that the second pole came into line with the other two points mentioned the man was facing at right angles to tho direction ho was taking when first observing the steamer, how far was he away from the vessel when he stopped ?

ONE FOR THE ARMCHAIR.

A man walks the full distanco between tho two places "X" and "Y" in a certain time at a uniform rate throughout, but if he makes the pace evenly over the whole distance at the speed of four and four-fifths miles an hour, he would complete the journey in twenty minutes quicker time. By adding to this statement that a uniform rate of walking or four miles an hour would enable him to travel the full distance in exactly one hour slower time than at the rate first mentioned, can the reader find without any extraneous aid in the form of pen or pencil', what the distance is between " X " and " Y" v ?

WIDOW AHD A WILL.

A recent judgment of the Supreme Court in tho case of a widow's application for the varying of a will, suggests a useful and interesting problem, though the actual figures are not based upon those mentioned in the judgment. Let it be assumed that tho value of the estate wa%, in round figures £16,000. which amount was directed to be divided between the widow, five sons and four daughters in certain proportions, instead of half of the estate going to a religious organisation. Now if each son received three times as much as a daughter, each of whom received exactly twice as much as the mother, can the reader find what difference the Court's judgment made in the amount received by the widow ?

DIFFERENT WAYS HOME,

A man resided some distance from tho city, his house being situated in a peculiarly favourable position so far as regards easy accessibility to three maiu roads leading to the city, as it is the same distanoe from three points of departure of service buses. Two of these stopping places, "X" and " Y," were on tha main highway, and were 330 yds. apart. From "X" to another stopping place, " Z," on another road, was 308 yds., and the third road between " X " and " 2 " 169 yds. in length. As it has been stated that the house is equidistant from these 'bus stops, how far were they away from the domicile ? There is an easy method of calculating this, which will be published next week. '*

LAST WEEK'S SOLUTIONS.

A Mining Venture.—£7so, there being 20 in the party at the commencement. Mistaken Instructions.—£2 16s. A Tethered Horse. The paddock formed two equilateral triangles, which mado it a simple matter to find the length of the tether, viz., 144ift. The use of a circle makes the solution quite obvious, the tether-post being tho centre. ,

Co-operative Milking.—As Brown milked four (not two) moro than his mate, his time was sixteen minutes longer than the lattor's.

An Ingonious Square.—First row, orvo eight, seven and a-half, two and Second row, six and a-half, three and a-half, four, five. Third row, four and a-half. five and a-half, six, three. _ Fourth row, seven, two, one and -vbivlf, eight and a-half. y ,

ANSWERS TO CORRESPONDENTS.

p,C.G.—Yon evidently took for granted that tho lengths of tho threa bases were the same, but that is not so. " Academy."—Yes, nil technical matter is avoided as far as possible. RX.—Hardly, as the restrictions limit the number. L.E.W.—Thanks for interesting lotter. " Two Allied Posers."—The explanation will bo deferred until September 27, in order to givo readers ample time to consider them. Erratum. In problem "In Three Directions'' (August 28), the lines were transposed, the "first being the fourth, and the others in succession being 7, 3, 1, 2, 5, 6.