More math puzzles and games

[...]... Mobius Band Take two strip s of paper and place them together, as shown Give them both a half-twist and then j oin their ends, as shown in the p icture We now have what seems to be p air of nested Mobius bands You can sh ow there are two bands by putting y our finger between the b ands and running it all the way around them till y ou co me back to where you started from So a bug crawling between the bands... 2 Routes, Knots, and Topology In fact all these puzzles are about the math of topology, the geometry of stretchy surfaces For a fuller description of what topology is about, see the puzzle "The Bridges of Konigsberg" on page 25 The puzzles include problems about routes, mazes, knots, and the celebrated Mobius band I n-to-out Fly Paths A fly settles inside each of the shapes sh own and tries to cross... The cuts are indicated on drawings a, b, and c In the last two puzzles, d and e, y ou need two Greek crosses to make up a squ are See if y ou can do it There is n o answer d e I nside-out Co llar Take a strip of stiff p aper and m ake it into a square tube A strip one inch wide and four inches long- with a tab for stick ing- will do nicely Crease the edges and d raw or score the diagonals of each... ore , Chicago , Detroit , an d E l Paso There are eight flights, a s follows : Baltimore to Chicago , Detroit to Chicago, Al b any to Baltimore , Chicago to El Paso , Chicago to Detroit , B altimore to Albany , Albany to El Paso , and Chicago to Albany What is the shortest way to m ake a trip from Albany to Detroit and b ack again? HINT : Draw a sketch m ap of the flights , beginning : A � B � C This... Paths This time the fly begins and ends inside each shape Can he cross each side once only ? The p ictu re shows he cannot do so on the triangle : He cannot cross the third side and end up inside Is there a rule here? No 17 A BC Maze Begin at the arrow and let y our finger take a walk through this m aze Can y ou p ass along e ach p ath once only and come out at A ? at B? and at C? Eternal Triangle? Can... them for ever and ever It would alway s walk along one strip with the other strip sliding along its back Nowhere would he find the " floor" meeting the " ceiling." In fact , b oth floor an d ceiling are one and the same surface What seem s to be two bands is actually Find out and then turn to the answer section to see if y ou were right As an added twist , having un nested the band( s) , see if... y ou how to avoid making too m any flights or getting stu ck in a "trap ! " Faces, Corners, and Edges Here is a surprising rule ab out shape s y ou should be able to puzzle out for y ourself Find a box-a m atchbox , a b ook , or a candy box , say N o w run y our finger along the edges and c ount the m ( 1 2) and add 2 to the number you found ( m aking 1 4) Now count the number of faces ( 6) an d add... done : Take a strip of p aper, ab out an inch wide and a couple of feet long J ust before j oining the ends, give one end a twist of one and a half turns (If you have read about the Mobius ban d , you'll k n ow this is like making one with an extra twist in it.) Then tape the ends togeth er to form a band That done, cut along the m iddle of the closed b and u ntil y ou come back to where you started At... cube The block was made out of a certain number of sm aller cubes and stood in the m iddle of a square plaza p aved with these smaller m arble cubes There were j u st as m any cubes in the p laza as in the huge block , an d they are all p recisely the same size Tell how m any cubes are in the huge block and in the square p laza it stands on HINT : One way to solve this is by trial an d e rror Suppose... one 8 central square , shaded, and several step-shaped j igsaw p ieces, each m ade up of three squares B y copying the grid and shading , c an y ou find how many j igsaw p ieces m ake up the complete grid? Then the number of squares in the complete grid sh ould be the number in each "j ig" times 8, plus I : I + ( 8 X 3 ) = 2 5 Next , i n grid c see i f y ou can copy and finish off the j ig­ saw p