Download e-book for kindle: Math without Words by James Tanton

By James Tanton

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High scorers are the brilliant (or sometimes lucky) scientists; poor scorers are the mediocre, impulsive (or sometimes unlucky) scientists who rush poorly confirmed theories into print. Dropouts correspond to the mediocre or overcautious scientists who prefer not to risk framing any conjecture at all. The Designer's score is twice the difference between the best and the worst scores of the others. His score is reduced if there are dropouts. Five points are subtracted for one dropout, 10 for each additional dropout.

It looks as if the pattern is symmetrical around the diagonal axis from top left to bottom right. Since no stars have appeared, Sackson induces that they are absent from the pattern. Now comes that crucial moment, so little understood, for the intuitive hunch or the enlightened guess, the step that symbolizes the framing of a hypothesis by an informed, creative scientist. Sackson guesses that the top left-hand corner cell contains a circle, that the three cells flanking it all have plus marks, and Patterns of Induction 51 that, continuing down the diagonal, the pluses are flanked by three-spot symbols, the pattern repeating itself with larger borders of the same three symbols in the same order.

You turn around and. after a few moments of feigned extrasensory corlceirtratiori. tell each person which object he took. The clue is provided by the number of matches remaining on the table. There are six possible permutations of the three objects in the pockets of the three spectators. Each permutation leaves a different number of matches on the table. If we designate the objects S , M. and L for small. medium, and large, the chart in Figure 11 shows the permutation that corresponds to each possible remaining number of matches.

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Math without Words by James Tanton

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