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vistaptb

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Posts posted by vistaptb

  1. Consider the points (x, 1), (x, 2), and (x, 3). If (a, 1), (a, 2), and (a, 3) have the same color combination as the x-points, a rectangle is formed because two of the x-points must be the same color. If these points are, say, (x, 1) and (x, 3), then the rectangle is between (x, 1), (a, 1), (x, 3), and (a, 3). Since there are an infinite number of x-values and only a finite number of color combinations for those three points, there must be two x-values with this same color combination and thus a rectangle.

  2. Basically, the question is, does a number have to be a multiple of (insert base here) to have a square that is a multiple of (insert base here)? I guess that statement would apply to

    5, 6, and 7 (4 squared is 20 in base 8, and 3 squared is 10 in base 9).

  3. I don't think the accused should be found guilty; two of the three judges would find him innocent. Say we extended this to 101 judges. If 50 judges say that the action is illegal but the defense didn't undertake it, 50 judges say that the defense did the action and that it was perfectly legal, and only 1 judge said that the defense was actually guilty, it would be ridiculous to convict him based on that.

  4. 100%. If the trees are x's and at two fixed points (which we established earlier), then the situation looks like this:


    l l
    l l
    x x
    l l
    l l
    The third tree must be between the lines to make an acute triangle and anywhere else to make an obtuse triangle. Thus, the probability of an obtuse triangle being formed is 100%.
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