ON GUARD!

New Zealand Listener, Volume 3, Issue 61, 23 August 1940, Unnumbered Page

ON GUARD!

HE Assistant PP (pro tem) is still struggling manfully with the ramifications of the problems and the correspondence on the same which have been bequeathed to him by the PP (who is still on holiday). After, hours of work over two particular problems which involved guarding six posts with guards, keeping a weather eye on a sergeant of guards, and talking about watches and whatnot with a guard on a train, he is convinced he was caught off his guard when he took over the whole business. Anyway, he is not going to attempt to solve any of the problems himself, but leaves that particular pleasure for the PP when he returns. And, by the way, when he does return, we have a bone to pick with him. We discovered it when digging around in his back garden, It was the missing solution to Crossword No. 19, so we've included it in The Page this week, And now for the answers to the problems in the issue of August 9: ANSWERS Condensed Crossword: BOSS ANNA SCAN KEGS Along the Waterfront: His number was 204, and the last of the row was 288. For the upper ten, who might prefer to work this sort of thing out’ according to the rules, we give Captain Cook’s method: If the number of my house be X and the last number of the row be Y then 14-2500 6 CK) Se (KS DY + (X+2) . .. + y; or: YCY+1) = 2Xsquared. From this the conditions under which 8Xsquared + 1 is a perfect square, must be examined. Within the restrictions imposed by the problem it may be seen that the X and Y values show an interesting pattern: X values Y values 0 0 1 af 2 3 4 5 6 8 35 49 204 288 1189 1681 6930 9800 The numbers 1 2 3 4 and 5 are inadmissible. Any value of X is 6 times the preceding one minus the one before that, while the Y in any term is seen to be given by the sum of its own X and the preceding pair. (49=35+6+8). Time for the Guard: This was the problem which Puzzled of Waihi Beach asked us to submit to public scrutiny since he did not know the answer himself. Neither does the PP (pro tem) so here is the only solution to hand. It was sent in by R. Martin, Glen Afton. After what looks like a nightmare of higher mathematics to the PP (pro tem), he arrives at the answer of 22 1/3 chains. He has even gone further and shown how the speed of the train can be calculated from the times given by the guard’s watch. He claims

it is 61-47/73 m.p.h, The PP (pro tem) doesn’t propose to question it. What do you think? Sentry Duty: The quickest way to change the positions of A and B is for the privates to move as follows: ABCADEACBDCAECDBA, This entails 17 moves, so the time for them to go off duty is 170 minutes past noon, which is 2.50 p.m.-(Problem and answer from G. Tisbury). PROBLEMS Kindergarten Finance Said Kitty to Harry, "Give me one of your halfpennies and I can buy an apple for baby and one for myself and you will have just enough money left to buy one for yourself." "No," replied Harry, "baby has no teeth, and could not eat an apple. You give me one of your halfpennies and

then you and I can each buy an orange and baby can watch us eat them." How many halfpennies did each have? -(Problem from R.J.G.). Condensed Crossword (Each word is of four letters) CLUES ACROSS: A girl and a mathematician’s favourite, Digs in the ground, Around a lagoon we drop an I. Do it again, as above and unknit "the ravelled sleeve of care." CLUES DOWN: Short for a happy time. Unintelligent-just pure memory. Worse than a lemon, If you can’t do this, don’t do what the dog does. One for the Tiny Tots Even the PP (pro tem) can work this one out, but he doesn’t know why it should be so. A farmer dies, leaving his three sons to share his seventeen horses | so that the eldest gets 12, the next gets (Continued on next page)

(Continued from previous page) 1/3, and the youngest 1/9. No horse must be left and each horse must be owned by one individual son. How is it done?-(Problem from R. Martin).

CORRESPONDENCE L.W.R. (Nelson): Sentries must have been bad boys! House number right. Answer to clock problem given issue August 9. Midnight on Wednesday. R. Martin (Glen Afton): Agrees with R.G. and says he believes that B looks out of the window at Papanui, but this would be impossible if he had alighted at Riccarton, as L.W.R. suggests. Thanks for the ‘""Time for the Guard" answer. Sentries right. Will use puzzles in due course. Thanks. ; R.J.G. (Waihi): He says, "I notice L.W.R.’s disagreement with my Five Travellers problem, but check proves me right. L.W.R. says B alights at Ricearton, whereas the puzzle says B looks out of the window at Papanui, which is the next stop past Riccarton! Other passengers likewise missed their stations or performed the impossible." Thanks for the puzzles. Pp Lillian (Hawera): Sentries right. Thank you. J.C.L. (Auckland): You will have seen the answers by now. Thanks for the puzzle. ‘""Newcomer" (Arthur's Pass): Crossword right. The spinning the coin business is beyond me! F.D.B. (Christchurch): Here's trouble! He writes "Thanks for printing my puzzle. I am sorry to have to tell you that you printed it wrongly, It should have read: Move No. 1 iece to bottom left hand corner occupied by o. 4. The way you worded it, it would appear to mean No. 1 piece to move to No. 4 square and No. 4 piece to No. 1 square. You will notice in the solution I sent you No. 4 piece was still near the bottom at the completion, and I think it is impossible to have both interchanged as you worded it." So what do puzzlers think now? .B. (Orangapai): Thanks for the puzzfe. G. Tisbury: Hastens to withdraw his remark about the Shunting Problem. His mistook the original position as meaning the original position of the truck. He asks us to accept his apologies for being so dense. Well, even Homer nods. H.G.L. (Taupo): Your letter and challenge received. The PP will be pleased to deal with this on his return.