ARE WE DOWN-HEARTED?

New Zealand Listener, Volume 3, Issue 69, 18 October 1940, Page 14

ARE WE DOWN-HEARTED?

N unusual dearth of correspondence last week (two letters when The Page went to the printers) makes that section look a bit thin this week. The PP hopes that this had nothing to do with the fact that during that period Parliament was in session, and the Burma Road came once again into the news. Don’t beat your wife if you get downhearted, or take to drink: write to Box 1070, Wellington, and your troubles will be multiplied immensely. What do you do when you’ve a headache? Stamp on your corn, of course. Once get worried about puzzles, and totalitarianism will look just about as important as it is. By the look of this week’s collection Stephen Leacock’s heroes, X, Y and Z, are into print again: PROBLEMS There is a batch this week from E. A. Vail, Hamilton. Thanks to this new correspondent, and here they are for you others:

The Defeated General After a repulse a general found that only 5,400 more than half his former force were fit for service, as 400 more than one fifth were wounded, and 500 more than one eighth were killed, missing, or prisoners. What was his force before the battle? Lazy Larry Larry walks to school travelling at the rate of 11 yards in 9 seconds, and is one minute late. If he had walked at the rate of 22 yards in 15 seconds he would have been half a minute early. What is the distance he goes to school? Alfréd and Barry Alfred is three years older than Barry. Eight years ago five-sixths of Alfred’s age exceeded three-fifths of Barry’s age by six years. What are their present ages? Books How many books can be bought for £5 if 17 cost as much over £2 as seven cost under £1? Ring the Change Here is a magic square. It adds 15 every way. You are required to make another nine-figure square adding to 15 but with the 8 in the position occupied bv the 9Q:

-(Problem from R.G., Waihi). ANSWERS (Refer to issue of October 4) Overboard: The level of the water fell, While it was in the boat, the iron displaced its own weight of water (through the agency of the boat). In the water, it displaced its own volume, a much smaller quantity. (Problem and statement from R.G.) Tricky Trains: This is Rob’s answer: Engine A goes into the siding with 20 trucks. Engine B runs along main line past the entrance to the siding and

pushes the remainder of the A train with it. Engine A then runs out of the siding with the 20 trucks. B comes back with its own train and the rest of A and deposits A’s trucks and van in the siding. It retires and goes on its journey. A comes back and picks up the rest of its train from the siding. All is now clear. Cucumbers: Eightpence each. (Problem and answer from R.C.J.M. Invercargill), Condensed Crossword: > 0 ARE Gt M PI REST Maths.: The trapezium can be inscribed in a circle. Half the sum of the sides is 29. From this deduct the length of each side to secure the lengths: 9, 13, 17, 19 rods. Multiplied together

these make 27,719. The square root of this is 194.4, which is the area in square rods. (Problem and answer from R.G., Waihi.) Triangle to Square: Let AB be the base of the triangle ABC. Now: Bisect AB in D and BC in E. Produce AE to F, making EF equal to EB. Bisect AF in G and with radius GA describe an arc to meet BC produced at H. Then EH is the length of the side of the required square. From E, with radius EH, describe an arc cutting AC at J. In the line from A to C draw JK equal to BE. From points D and K drop perpendiculars to points L and M on the line EJ. The required four pieces are BDLE, DLJA, JMK, and KCEM, (Problem and answer from R.C.J.M., Invercargill). It is suggested that readers prove this solution by theory.

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