SAVE THE SCISSORS!

New Zealand Listener, Volume 3, Issue 68, 11 October 1940, Page 14

SAVE THE SCISSORS!

N The Page this week we present a picture of a pair of scissors in captivity. Readers are expected to get them free, and without more ado they are invited to go to it. PROBLEMS Scissors in Captivity This represents a pair of scissors, with a piece of string looped as shown. The problem is to get the scissors free

while someone else holds the free ends of the string at A. (Problem from S.G.E.) Three Little Girls Fifteen girls in a private school were taken each day for a walk. Every day they walked in five ranks of three. The mistress wished to see that they mixed well and wanted to arTange them so that, for seven con-

secutive days, no girl would walk more than once with any of her schoolfellows in the same rank. How did she do it? (Problem from E.A.C.) Xercise "A little exercise in logic, no trial and error!" says AJAS, whose problem this is. He was _ inconsiderate enough to leave the answer in Dunedin. If mext week-end is fine and sunny, it’s not an absolute certainty that the PP will have the answer next week:

Farm Finance Three chickens and one duck were sold for as much as two geese. One chicken, two ducks, and three geese were sold for 25/-. What was the price of each bird in an exact number of shillings? (Problem from R.C.J.M.)

ANSWERS (Refer to Issue of September 27.) Rhyme for Time: Mother of Two, who sent the problem suggests June 1, 1928, June 8, 1929, June 15, 1930, and June 23, 1931, as the dates of the first birthdays. Take the Count: Level, 40 times; ada 56. (Problem and answer from R.G.). Men g0 Shopping: 13/6. (Problem and answer from R.C.J.M., Invercargill.) Keep it Down: (Problem and answer from R.C.J.M.)

This note on the problem is supplied by S.G.E.: "These problems are known as unicursal problems, from the Latin unus, one; and curro, I run. Interest in them was first started by the work of the great Swiss mathematician, Leonhard

Euler (1707-1783). The points where the lines meet are called "nodes," and the node is said to be single, double, triple, etc., if one, two or three etc, lines meet at it. A single node is sometimes called a free end. Euler’s theorems are as follows: (1) ‘In any network the number of odd nodes is even.’ (2) ‘In any closed network, with no odd nodes we can completely describe it unicursally from any point and finish at the same point’, (3) ‘A figure which has two and only two odd nodes can be completely described unicursally, but we must start at one of the odd nodes and finish at the other!’ (As in the problem above). (4) ‘A figure which has more than two odd nodes cannot be completely described in a unicursal route.’ "These theorems," S.G.E. comments, "are remarkably easy to prove. Perhaps they could be set as problems. You will see that they furnish us with a set of rules by which we can tell at a glance whether any given figure can be traced unicursally, and, if it can, where to start from." (Continued on next page)

(Continued from previous page) No doubt the doodling type of Puzzler will dispense with S.G.E.’s methodical recommendations, but we thank him on behalf of all those precise mathematicians who like things done by rule. S.G.E. has certainly paid his fee. CORRESPONDENCE R.G. (Waihi): Welcomed W. Robinson’s statement of the working for Time for the Guard, "which shows me my error, so I humbly make my bow to him." R.G. will see that other correspondents have other ideas. He sends an exercise in word building used as a problem this week. R. Martin (Glen Afton): Comments concerning Time for the Guard that the van may not have passed, the clock while it was striking. In which case it would have travelled 440 feet in 28 4/5 seconds, and if this were so the train would be 1,356 2/3 feet long as X.G.T. said. "Humblest apologies to W. Robinson for saying he was wrong." R.M. correctly answers Farm Labour and adds that if some of the men wanted a spell 12 could work in each corner section, giving a minimum of 48 possible under the conditions. We are afraid, however, that the farmer would notice the four empty sections. And R.M. seems to have under-estimated the versatility of our hostess. Other answers correct, and readers who have not seen it in The Page before may like to work out R.M.’s query about how much a brick and a-half would weigh if a brick weighed a pound and half a brick. J.C.C, (Timaru): Points out, with reason, that the sentence "I saw rats live on" is not strictly a palindrome, but he should remember that we also printed its reverse, so that he would get a palindromic group of words if he read the reverse in reverse and reversed the original. However, we're wriggling, and admit it. J.C.C. offers these true palindromes: MADAM I’M ADAM. SNUG RAW WAS I ERE I SAW WAR GUNS. J.C.C., for sending the puzzle, but we've had it before. S.G.E. (Glenavy): Is corresponding at length with H. G. Lambert of Taupo, and seems to be enjoying himself no end. As fee for our "introduction bureau," as he calls it, $.G.E. sends a problem about scissors and a note on unicursal problems. Readers who want to know what that means will have to read the note, printed with the answer to ‘‘ Keep it Down." Thank you, 8.G.E. AJAS (Dunedin): When you mention ladders the trepidation is all on our side. But we can take it, so welcome to you and thanks for the puzzles. As they seem to be most suited to the specialists we give them here: "The chord of a circle is one half mile long and the arc is one foot longer. Find the mid-ordinate." And another one like Pat and the Pig: "A fox starts running due east with a constant velocity. A hundred yards north, a dog starts running at a constant speed, changing direction constantly so that he always runs directly towards ;

the fox. Just as the fox finishes running his three hundredth yard the dog catches him. How far does the dog run? J.S. (Putaruru): That was cortatalyy a technical point. See below. Lillian (Hawera): J.S., of Putaruru, would like to write to you. Uncle Peter will send the address if you feel chummy. Rob (Ahipara): R.C.J.M., who set the problem, disagrees about Battle and His answer was 472. You were correct for Men Go Shopping but ‘"level’’ seems to be the cause of some disagreement. Thanks for the encouraging note, X.G.T. (Koptawhara): Top of the class for a model paper. By the way, what does "X.G.T." stand for? E.A.C. (Wellington): Equal for answers with X.G.T. and ten extra marks for sending a problem.

A.G.L. (Taupo): Has found time between writing letters to $.G.E. to sum up the Time for the Guard problem. Actually, he had done this before, in the days of the Ass-PP, but the letter is buried among the archives and our staff of archeologists has not yet unearthed it. Mr. Lambert says that there are two possible answers to Time for the Guard. One of them is 440 feet. The second arises from presuming that when the guard heard the last stroke he still had not yet reached the bridge. This gives a very slow speed for the train, and quite a long length, but within the bounds of possibility. A.G.T. (Picton): Puts pen to paper to back up W. Robinson’s answer to Time for the Guard. He says 440"feet, too, and adds a note of appreciation for the fun he gets out of playing with the miscellaneous puzzles which readers send in. Puzzlers please mark A.G.T. as one of the brethren, although he has not yet paid his fee. One puzzle from Picton please.