Intellect Sharpeners.

New Zealand Herald, Volume LXVIII, Issue 20792, 7 February 1931, Page 5 (Supplement)

Intellect Sharpeners.

PROGRESS OF THE SNAIL.

BI T. L. BRITON.

Two snails reposed in a rectangular card* board box in an unused shed. The box, which had no lid, was 30in. long and 18 wide, with a depth of 4in., and was lying proper side up. One of the molluscous sluggards was then hibernating afc one end of the box, while the other was moving from the opposite end toward him, the incident prompting a problem. Draw two circles of equal size on the floor of the box, one at each end, so that the long side as well as the short ones form two tangents of the circles, the other long sido of the box being some distance from the circumferences. The sleeping slug was at the exact centre of one circle, and its mate was within the other at a point Bin. in a direct line from one tangent, and 9in. from the other also in a direct lino It then moved toward the other snail in a direct line, resting on the circumference of its own circle. The question for the reader to answer is: How long would it take slug No. 2 to reach its dormant brother, starting from the last-named point, if it progressed at tho rato of an inch in 12 minutes ?

A FLOWING TIDE. Two boats with slow mechanical speed started off together from the same point,, ono of them, " X," proceeding down stream with the tide, while the other, "Y," travelled irj a direct opposite course, tho respective routes being south and north. At the end of three and threequarter minutes the two boats were exactly 1100 yds. apart, when "X " turned and followed in the same direction as the other boat. At the expiration of , 12£ minutes from the moment that " X " turned back, the total distance covered by the two craft was three times as much as the formerly-mentioned distance. Assuming that the boats, as well as ifea tide, maintained their own individual speeds throughout, the latter in the one direction, can the reader say at what rate the stream flowed, taking for granted that there was no perceptible delay in turning " X " boat north ? 6 \ TWO WATERMEN. While on the water let us take the case of two watermen who rowed a race in heavy skiffs. "X " was given a start by his opponent, " Y," which was equivalent to the distance that " Y " propelled his boat in 10 strokes, which, like the other rowers, w;ere uniform throughout the contest, although at different rates, ' X " took four strokes to " Y's " five, but* that, five of the strokes oi: X occupied exactly the same time as six of those made by " Y." With these few details, as the basis of calculation can the reader find, perhaps without the aid of pen or pencilj how many strokes must " Y " make before he catches his opponent, which it is obvious he did as no mention is made as to the distance of the race? . i A BOARDING SCHOOL. In this 'establishment, 30 boarders con. stitut.e the normal "strength," and, although " day-boj's " take lunch at tlhe school, that phase of the matter does not concern this problem. In such institutions, careful records are kept of expenditure, and upon these figures in the present case this problem is based. cepting 30 as the average number in residence, the records show that an addi- 'i . tion of five boarders increases the gross annual expenditure by £3OO, but at the same time it diminishes the Average cost per head by £l. Upon thfese figures can the reader find what the annual expenditure is when the establishment has the normal number of boarders, viz, 30 ? This is a practical question, likelwi.,,to be met daily. " EXACT." "Here is a little counter problem which may give the reader 10 minutes of :in- , tellectuaL amusement. Make a diagramoo s an oblong and divide it first into two equal parts by a line joining the two short ends, and each of these parts into three others of more or less equal size, making six " squares " altogther. Number these one to six, reading from left to right. Then take five counters, lettered respectively, Capital E, x, a, c, and. t, placing E on 1, t on 3, c on 4, a on 5 • and x on 6. -The problem is to mcve these counters in accordance with the following so that the letters ' will read " Exact," leaving the first space blank instead of the« second one. Counters are to be moved one at a time perpendicularly or horizontally to a blank ' space adjoining the counter 'moved. No jumping over another counter is permissible, neither is a diagonal move allowed. A counter may not be removed from the board to permit another to take its place temporarily, and no space may be occupied at the same time by more than one counter. Under these conditions what is the fewest number of moves necessary to achieve the desired result? LAST WEEK'S SOLUTIONS. Simple Yet Puzzling.—Five boys 25 girls and 70 infants. For the Counting House.—Ten halfi sovereigns, 40 half-crowns and 24 florins, making a total of £l2 8s will meet the case. Taking Chances.—Ten pounds invested on " A," £7 10s on " B " and £6 on " C," would yield a profit of £6 10s no matter which horse won. Passing Starting Points.—Adam. had passed his starting point three times, and Boyd his twice, before tho former caught up to tho other, which occurred at a point 66 2-3 yds. from where Adam started. Three Each Way.—The formula is:— N square, plus three N, plus two, multiplied by N square, plus three N, .plus three, and divided by six. The number required is represented by N. f ANSWERS TO CORRESPONDENTS. A.S.B.—Thanks for memo. Comments are appreciated. " Rifle."—The gun would fire 60 shots in 59 minutes i£ it fired one a minute. " Curious."—There was an added con- ;; dition that the four parts should be of the same shape and size. Thanks. " Pencarrow.—Named after the place of residence in Cornwall of Sir William Molesworth. Palliser Bay after Sir Hugh Palliser. " Inquirer."—Martinique was captured by Britain from Spain in tho year 1762, at the time of the capture of Manila, Havana, etc. D.F.G.—An equilateral triangle is always acute-angled, but an isosceles triangle may be apute-angled, obtuse or right-angled. See issue 6/12/30. " Query."—There are several ways of solving the puzzle you mention. A problem will appear later emlbodyiing a condition which will limit it to one solu k tion. Jm M