Mathematical Circus: More Games, Puzzles, Paradoxes, and Other Mathematical Entertainments from Scientific American
Martin Gardner
Language: English
Pages: 272
ISBN: 0394502078
Format: PDF / Kindle (mobi) / ePub
Stated: First Edition. Pages are clean and binding is tight. Slight tanning to top page edge. DJ price clipped at top flap.
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scores 12, B scores 7, and C drops out with a score of 0, FIGURE 25 Three stages in probing for the Master Pattern D's score is 19, or twice the difference between 12 and 0, with five points deducted for the single dropout. If A scores 12 and B and C both give up7 D scores 9. This is twice the difference between 12 and 0, with five points deducted for the first dropout, 10 for the second. If all three players drop out, D's score is -25. His basic score is 0, with 25 points subtracted for the
step. A man begins the walk at spot 0. He flips a coin to decide the direction of each step: heads he goes right, tails he goes left. In mathematical terminology his "transition probability" from one mark to the next is 1/2. Since he is just as likely to step to the left as to the right, the walk is called "symmetric." Vertical bars A and B, at -7 and +lo, are "absorbing barriers." This means that if the man steps against either barrier, it "absorbs" him and the walk ends. A novel feature of this
line means balance, a slanted line shows how the scale tips. 7. The only answer is 6,210,001,000. I do not have the space for a detailed proof, but a good one by Edward P. DeLorenzo is in Allan J. Gottlieb's puzzle column in the Massachusetts Institute of Technology's Technical Reuiew for February 1968. The same column for June 1968 has a proof by Kenneth W. Dritz that for fewer than 10 cells the only answers in bases 1 through 9 are 1,210; 2,020; 21,200; 3,211,000; 42,101,000, and 521,001,000.
of 300. The repeating cycle is 1,500 for three final digits, 15,000 for four digits, 150,000 for five, and so on for all larger numbers of digits. 5. For every integer m there is an infinite number of F-numbers that are evenly divisible by m, and at least one can be found among the first 2m numbers of the Fibonacci sequence. This is not true of the Lucas sequence. No L-number, for instance, is a multiple of 5. I Fibonacci and Lucas Numbers 161 6. Every third F-number is divisible by 2, every
consist entirely of pairs, with no extra match left over. "Count" the other pile in the same way. After the last pair has been slid aside a single match will remain. With convincing patter the trick will puzzle most people. Actually it is self-working, and the reader who tries it should easily figure out why. A trick that goes back io medieval times and can be found in the first compilation ever made of recreational mathematical material, ProbL&zes plaisans et d&lectable.s.by Claude Gaspar