Evening Star Newspaper, July 24, 1932, Page 66

[SUEE————— THE SUNDA¥ STAR, WASHINGTON, D. C, JULY 24, 1932. rain Battlers Test Your Thinking Cap BY GEORGE H. DACY. HE roster of those who answer the challenges “of - perplexing - brain bafflers and modern mathe- matical magic runs the full gamut of human occupations, for the en- ticements of these intriguing enigmas spur millions daily to don their thinking caps in order to wrestle with the cranium crump- lers. Scientist, sailor, lawyer, logger, doctor, door- man, professor and pipefitter—all on the grounds of a common brotherhood match wits against the wizardy of the testing brain teasers. There is nothing better adapted to eliminate coenceit from him who poses as a wise man than several rounds of concerted thinking mus- tered for the solution of some of th2se stub- ‘orn mentality testers. Some seek to belittle the puzzle games and figure riddles as brain balderdash. They refuse to compete with the think-cap testers. How- ever, the overwhelming majority of those who rcad and seek fascinating diversion during idle hours are ardent fans of me magic. The popularity of the cranium ticklets is based largely on their versatility. They range from clever conundrums which schoolboys can solve to puzzlets which bewilder even the leading masters of mental attainment. American ad- vertising now is capitalizing on the lure of this puzzle age by staging such a multiplicity of prize conte s never previously temnted the “nut cracking” talents of any country. Government entists and teachers have long used puzzie games and mathematical riddles as mediums of diversion and amusement. Many of them gain similar idle hour and spare time pleasure from solving the “cranium challengers” as their amatcur craftsmen associates veap from shopwerk., home mechanics and related hobbies. George H. Wardlaw of the National Bureau of Standards has gone so far in his mathe- matical magic quest as to devise 71 original puzzle tricks with matches. To most of us a box of matches is nothing more than 58 tiny sources of tinder in a small container. Mr. Wardlow has hatched out a plethora of inter- esting and entertaining tricks from that dally and unassuming occupant of one of your pock- ets His ingenion: game of Chinese chess played with match sticks is founded on the mathe- matical Jaw of balanced components. With three unequal piles of matches on the board, A can always get into a position to win by the stmpie expedient of separating each pile into its components in terms of the powers of 2, and then making these components balance. That is to say, the piles can be separated into groups of 1, 2. 4, 8, 16 and so on. The majority of the Wardlaw brain brushers consist of puzzle outlines such as squares, stars, triangles and other geomctric figures formed with matches, the test being to shift certain of the matches in order to form other figures. For example, make five squares of 16 matches and then by shifting six matches form four equal squares. Form an equal-sided tri- angle of nine matches and then shift five matches and form five equal-sided triangles. Make a five-pointed star with 10 matches. Take away four matches and form a six-pointed star. Form a six-pointed star with 18 matches and then by shifting six matches convert it into a snow crystal Porm three diamonds from 10 matches. Make three matches appear as four without breaking them. With six matches make a bridge that will span a stream wider that the length of one match. A mathematically-minded, man has some matches in a box. Asked how many matches he had, he replied: “If the number of maiches in this bcx were only half as many as I should like to have, then there would be 10 more matches in it than twice as many as there really are in it. And, again, if there were four more matches in it than there really ave, and I should add four additional matches to the mumber I should like to have, then the total number of matches I should like to have would be five times as many as the actual number of matches in the box when the four matches are added to it. How many matches are in the box? A shipwrecked crew contains 19 whites and a Malay. Food becoming low, they draw lots to find who is to be sacrificed. They stand in a row and agree to let the skipper count out each sevanth man. Which man did the skipper begin with so as to make sure that the Malay would be the one to go? In solving this problem. let 20 matches represent the crew and the Malay. ERE is a simple test for the money changer which Mr. Wardlaw asked your writer. A man stopped me on the street the other day and asked me if I could change a bill so that he could get a nickel for a telephone call. I told him that I was unable to change a $1 greenback so that he could obtain a 5-cent piece but that I could change a $5 bill so that he could get the desired nickel. How did I Inake the change? The distance between Washington and Bal- timore is 40 miles. A bicycle rider, A, riding at the rate of 12 miles an hour leaves Washington at the same time that another bicyclist, B, riding at a speed of 1425 miles an hour, leaves Baltimore. A wasp flying at the rate of 16 miles an hour stings rider A as soon as he mounts his wheel and then flies back and stings rider B. The wasp repeats its performances, oscillating between A and B until they meet. ‘How far did the wasp fly? Not so long ago, the civil service presented the following mentality tickler as one of the questions of an intelligence test for trained economists desired in the Government service. The names of three passengers on a certain train were Mr. Jones, Mr. Smith and Mr. Robin- son. The fireman, engineer and brakeman on that particular train were also named Jones, Smith and Robinson. Mr. Robinson lives in Detroit. Smith can beat the fireman playing killiards. Mr. Jones earns exactly $2,000 s year. The brakeman lives midway between Detroit and Chicago. The passenger who lives in Chi-~ brakeman’s nearest neighbor, one of the pas- Fun With Puzzles and Figures Formed From Modern Muthematical Magic—Popularity Is Based Largely on Versatility. Devotees of the peg puzzle games have originated 120 different methods of intricate play. sengers, earrns exactly three times as much as the brakeman. What is the engineer’'s name? An animal trainer dicd, willing his entire estate, which consisted of 17 el:phants, to his three children. as follows: One-half to the youngest of the three, one-third to the next. and ome-ninth to the oldest. How was the division actually made? Five men with a monkey as mascot were gathering coconuts on a tropical island. When they finished the harvest they placed the nuts together in ome huge pile. Then the tired pickers went to sleep. One man dreamed that his mates intended to cheat him of his full share so he awakened early, stol: stealthily to the nuts, divided them into five equal lots, concealed his share and tossed one odd nut which was left after the division to the mon- key. and then heaped the other nuts together. Then the man returned to his slumber. Shortly afterward, the second picker, suspicious of the honesty of his companions. arose and divided the coconuts into five equal piles, removed and hid his just share and gave one nut that was left over to the monkey. Thereupon, number two piled the nuts that rematned in one group and returned to his blanket. Subse- quently, the other three pickers, in turn, did likewise, and returned to their bunks. The next morning after breakfast the five men divided the coconuts egually among themselves. One coconat that remained after that division was thrown to the monkey. Altogether th> monkey received six coconuts. How many nuts did the pickers get? Here is a mathematical teaser which in- volves plenty of pencil work but which can. be solved. A ladder is leaning against the wall of a house which is 12 feet high. A box four feet wide is placed under the ladder so that it touches both the ladder and the wall of the house Frcem the point where the box touches The estate was to be divided the ladder to the ground measured along the ladder is also four feet. How long is the ladder? UST down the hall from Mr. Wardlaw’s office at the Bureau of Standards is that of Mr. 8. B. Detwiler, jr., another Federal expert who devotes his spare time to the solution of math- ematical riddles and puzzles founded on the laws of permutation, geometrical progression, magic squares, unicursal problems, shunting and the like. Here are a few of the “brain per- plexing gems™ which Mr. Detwiler had on tap for the mental confusicn of all who wished to vie with such. . do not like . . said the man with the white . . . The . . . . is impressive but when you . . ... a man, you . a . . . ... . power of memory. There will B el from and the . . of this will be recognized. The first blank space in this puzzler represcnted by one dot is to be filled in with a word of onme letter, the second with a word of two letters, the third with 3 letters, and so on. The last blank space is for a 10- lettcr word. The first letters occur in all the words, the second oecurs in all the words be- ginning with the second word to be filled in the two-dot space, while the third occurs in all the words beginning with the third unfilled space, and so on. The paragraph as com- pleted pertains to one of the scven sacraments, A room is 30 feet long, 12 fect high and 12 feet wide. Along the middle line of one of the sidewalls and 1 foot from the ceilint is a wasp. On the median line of the opposite wall 11 feet from the ceiling is a fly. How long is the shortest route which the wasp can This puzzle of position is one of the most difficult to solve. It consists of 15 parts of diffevent shaped metal which fit together so form a checkerboard. follow in traversing walls, ceiling or floor of that room in order to reach the fly? Here is a simple little mentality tester which you can try out most anywhere as the only pawns needed are copper pennies and a similar number of nickels and dimes, or either. Place the coins on a row of six squares and a blank drawn with a pencil on a strip of paper. Now move the coins one at a time, the pennies to the right and the silver always to the left. You can move into the adjoining space if it is vacant or you can jump a coin if the square beyond is unoccupied. The idea is to alter- nate the original pcsition of the coins, placing the pennies where silver coins were, and vice versa. Fiftcen moves are required to make the interchange. Another simple edition of coin magic con- sists in the use of four nickels and a like number of pennies. Arrange the coins in a row, first the four pennies in sequence and then the four nickels. The test is then to move two coins at a time—each pair that touch maintaining such relationship through- out all the maneuvers—until the position of the coins is alternated, so that their arrange- ment is nickel, penny, nickel, penny, and so on. Position of coins at the start of this riddle is: Pennies Nickels b § 2 3 4 5 6 7 8 0 0 o0 o 0 0 o0 o You can create a distinct illusion with a double cone and two sticks which will mysiify observers until the working principle of the trick is explained. Make two cones with bases 2 inches in diameter and 3 inches high out of soft wood and ccment the cones into one piece by glueing their bases together. Make an in- clined track with the junction of the sticks or rails on the floor or table. Then roll the double cone down that plane and it will look as though it is ascending the incline. This is because the center of gravity of the double cone is moving in a vertical plane bstween the two sticks. It occupies a lower position as the points of contact on the sticks get higher. Hence as the cone rolls up the sticks, its center of gravity descends. Learned mathematicians as well as adept chess players who have performed the following feat recommend it to your attention if you are interested in chessboard befuddlers. The object is to place a knight at & given position on the boz:d and then move it so that it occupies all possible positioris on the game board once and finally ends up at the starting point. This requires 65 moves and plenty of the strategy and thinking which dignify the successful solver of brain teasers such as this one. During early times, magic squares were used by certain of the ancient seers soothsayers as the foundation of their fortune- 1ling. Even today the puzzle fan can reap amusement and recreation from magic squares of either an odd or an even number of spaces. Here is a simple test of your prowess with numbers. Draw a 4-sided 16-space square and then attempt to arrange the numbers from 1 to 16 in that square so that the sum of the figures in the diagonal extending from the lower left hand to tne upper right hand corner will equal the sum of the figures in the diagonal from upper left hand corner to the lower right hand corner of the square. The magic square puzzle is more difficult to solve if an even number rather than an odd number squares is used. PROBLEMS in permutation and combination are common in certain classes of cranium perplexers. Fifieen players on a base ball squad waik in trioé from their hotel to the training fleld twice daily for spring practice for one month. Presupposing that no single player walks in a group of 3 with any other given player more than once, how many trios can the 15 players be divided into? Practical puzzles of wood which are held together by key blocks and interlocking joints are now available for testing the ingenuity of those who believe that everything can be solved if you only attack the riddle persistently in the right way. ingcnious Japanese craftsmen lead the world in the origination, production and distribution of these brain besters. No di- rections accompany these puzzies. The “catch” is for the purchaser to dissemble and then as- semble the wooden device again without mis- cues or mistakes. Each puzzle is a faithful product of the laws of permutation and com- monsense. It may be a perfect cube composed of 15 or 17 interlccking blocks of wood held to- gether with a key block. Sometimes the cube is made more bizarre by beveling all its corners. Another popular puzzle of similar construction is made in the form of a warship, two of the guns in this case being the key blocks. The only way to solve these condundrums worked in wocd is to study them painstakingly as you first dissemble them after purchase. Many modifications of the famous 15 puzzle are now played with daily by the young and old, unschooled and highly educated fans in all parts of the world. The original 15 was a teaser composed of 15 numbered blocks in a flat box designed to accommodate 16 such blocks. The pu of this riddle was to move the blocks about MRe checkers without lifting them from the container in such manner that the number 15 block would occupy every posi- tion on the board in numerical succession. This is a real test of any player's skill and patience. Modificaticns have reduced the number of blocks to seven in some of the new styles by doubling and even quadrupling the size of some of the blocks. Fifty-e‘’ght moves are necessary with this revised equipment to “work” the baf- fler correctly. Puzzle peg has won many devotees among those who gain fun matching wits against the pegholes. To one are occupied by small wooden pegs. idea is for the player to jump intervening and thus remove them from field of