Mathematical Magic Show
Martin Gardner
Language: English
Pages: 297
ISBN: 0883854481
Format: PDF / Kindle (mobi) / ePub
How do you move two matches - and only two - to new positions, so that the glass is reformed in a different position, with the cherry outside? This is one of those rare puzzles that can be solved at once if you approach is correctly, but intelligent people have been known to struggle with it for 20 minutes. The author provides the solution. The treats in this book range from Moebius bands to coin and card trickery, from finger arithmetic to the post-Ticktacktoe game of Tri-Hex.
New York Magazine (16-22 November 2015)
Kerrang! [UK] (31 October 2015)
The New York Times (1 September 2015)
-1 and B's minmax is 1, it is clear there is no saddle point. Consequently neither player finds one strategy better than the other. It would be foolish, for example, for A to adopt the strategy of always showing two fingers because B could win every time by showing one finger. To play optimally each player must mix his two strategies in certain proportions. Ascertaining the optimal proportions can be difficult, but here the symmetry of this simple game makes it obvious that they are 1 : 1. This
card: a red two pasted to a black seven. Each chooses a side of his card and simultaneously shows it to the other. A wins Game Theory, Guess I t Foxholes 39 if the colors match, B if they fail to match. I n every case the payoff in dollars is equal to the value of the winner's card. The game looks fair (has a value of zero) because the sum of what A can win (8 1 = 9) is the same as the sum of what B can win (2 7 = 9). Actually the game is biased in favor of B, who can win an average of $1
off your wrist, cut the rope, or tamper with either of the existing knots. The trick is not well known except to magicians. FIGURE 18 Rope for the knot problem ANSWERS I. FIGURE19 shows how two matches are moved to re-form the cocktail glass with the cherry outside. 2. If overlapping of paper is not allowed, the largest cube that can be folded from a pattern cut from a square sheet of paper with a three-inch side is a cube with a side that is threefourths of the square root of 2. The
with odd half-twists but all of them are homeomorphic with one another [see Figure 391. More strictly, they are homeomorphic in what topologists call an intrinsic sense, that is, a sense that considers only the surface itself and not the space in which it may be embedded. It is be- FIGURE 39 Strips with odd (left) and even (right) numbers of half-twists Mobius Bands 125 cause our model of a Mobius strip is embedded in 3-space that it cannot be deformed to its mirror image or to a band with
and SOLOMON W. GOLOMB'S book Polyominoes, published by Scribner's, stimulated worldwide interest in these figures: polygons formed by joining unit squares along their edges. This interest in turn led Golomb, who teaches electrical engineering and mathematics at the University of Southern California, to devote more of his off-duty hours to exploring some of the darker corners of the field. A communication from him deals entirely with a series of fascinating problems, only partially solved,