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Math Help - Need help: weights problem

  1. #1
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    Need help: weights problem

    You are given N weights, the first weighs 1 pound, the second 2 pounds, and so on (the N weight weighs N pounds)ץ
    You are given an N-binary-word that's formed by L's and R's and scales.
    You need to provide an algorithm of N steps, which in each step puts a weight on on of the scales (the left or the right one), and that in the i-th step the scales will lean left if the i-th letter in the word is L and will lean right if it's R.

    for example: if N=3 and the word is LLR then the algorithm should say:
    1. put 2 on the left scale
    2. put 1 on the right scale (the scales will still lean to the left)
    3. put 3 on the right scale



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  2. #2
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    Re: Need help: weights problem

    I have no algorithm more sophisticated than trying the combinations and seeing what happens.
    Here are the results for 7 weights that minimize the amount of imbalance in the scale.
    Note that negative numbers represent a weight placed in the left pan; positives go on the right.
    To get the combinations where the scale tips right first, reverse the signs.

    LLLLLLL -7 6 -5 4 1 -3 2
    LLLLLLR -6 5 -3 2 1 -4 7
    LLLLLRL -5 4 -3 2 1 6 -7
    LLLLLRR -6 5 -3 2 -4 7 1
    LLLLRLL -5 4 -3 2 7 -6 -1
    LLLLRLR -4 3 -2 1 6 -7 5
    LLLLRRL -5 4 -1 -2 6 3 -7
    LLLLRRR -6 5 -3 2 7 -4 1
    LLLRLLL -5 4 -2 6 -7 3 -1
    LLLRLLR -4 3 -2 7 -6 -1 5
    LLLRLRL -3 2 -1 6 -7 5 -4
    LLLRLRR -4 3 -2 6 -7 5 1
    LLLRRLL -5 4 -3 6 2 -7 1
    LLLRRLR -4 3 -2 5 1 -7 6
    LLLRRRL -5 4 -2 6 -1 3 -7
    LLLRRRR -6 5 -4 7 2 -3 1
    LLRLLLL -5 4 6 -7 1 -3 2
    LLRLLLR -4 3 5 -7 1 -2 6
    LLRLLRL -2 1 4 -7 3 5 -6
    LLRLLRR -4 3 5 -7 1 6 -2
    LLRLRLL -3 2 5 -7 6 -4 -1
    LLRLRLR -2 1 5 -7 6 -4 3
    LLRLRRL -2 1 5 -7 4 3 -6
    LLRLRRR -4 3 5 -7 6 -2 1
    LLRRLLR -5 4 6 -2 -7 3 -1
    LLRRLLR -1 -3 5 4 -7 -2 6
    LLRRLRL -1 -2 4 3 -7 6 -5
    LLRRLRR -4 2 6 -3 -5 7 -1
    LLRRRLL -5 3 7 -4 2 -6 1
    LLRRRLR -4 3 5 -2 1 -7 6
    LLRRRRL -5 3 6 -2 -1 4 -7
    LLRRRRR -6 5 7 -4 2 -3 1
    LRLLLLL -5 7 -6 2 1 -4 3
    LRLLLLR -4 7 -5 -1 2 -3 6
    LRLLLRL -1 4 -7 3 -2 6 -5
    LRLLLRR -4 7 -6 2 -3 5 1
    LRLLRLL -4 6 -3 -2 7 -5 -1
    LRLLRLR -1 4 -7 3 2 -5 6
    LRLLRRL -4 7 -5 1 2 3 -6
    LRLLRRR -4 7 -6 2 5 -3 1
    LRLRLLL -2 6 -7 4 -5 3 -1
    LRLRLLR -1 4 -7 6 -5 2 3
    LRLRLRL -1 5 -7 6 -4 2 -3
    LRLRLRR -2 6 -7 5 -4 3 1
    LRLRRLL -2 6 -7 4 3 -5 -1
    LRLRRLR -1 4 -5 3 2 -7 6
    LRLRRRL -3 7 -6 4 -1 2 -5
    LRLRRRR -4 7 -5 6 -3 2 -1
    LRRLLLL -5 6 4 -7 1 -3 2
    LRRLLLR -4 6 1 -7 3 -2 5
    LRRLLRL -4 7 -2 -3 1 5 -6
    LRRLLRR -4 6 1 -7 3 5 -2
    LRRLRLL -4 5 2 -7 6 -3 -1
    LRRLRLR -1 2 3 -7 6 -5 4
    LRRLRRL -4 5 2 -7 6 -1 -3
    LRRLRRR -4 5 3 -7 6 -2 1
    LRRRLLL -5 6 3 -2 -7 4 -1
    LRRRLLR -4 7 -2 3 -6 -1 5
    LRRRLRL -2 4 -1 3 -7 6 -5
    LRRRLRR -4 7 -2 3 -6 5 -1
    LRRRRLL -5 7 2 -3 4 -6 -1
    LRRRRLR -4 6 1 -2 3 -7 5
    LRRRRRL -5 6 1 2 -3 4 -7
    LRRRRRR -6 7 5 -4 2 -3 1
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