30 Jun '07 17:47>
What is the least number of weights that can be used on a set of scales to weigh any whole number of kilograms from 1 to 40?
Originally posted by SwissGambitYou don't happen to have a copy of "Fermat's Last Theorem" do you?
I wrote a prog to work it out first, then I figured out why it works.
The bias of the scale is simply the weight on left minus weight on right. I must be able to bias the scale from 1-40 kg, per stipulation.
To get the most use out of each weight, we use it in each of its three possible positions: right, left, or off-scale.
1 kg is the natural s ...[text shortened]... = 40kg, which solves (and reveals why the problem's creator chose 40kg as the upper limit).
Originally posted by crazyblueWhat method do you use? I believed the maximum to be 12, unless you know beforehand if the odd weight is heavier or lighter. With 13 balls there is a chance you don't find out if the odd ball is heavier or lighter.
some years ago i did some thinking on that find-the-odd-ball-in-3-measurings-problem. hope you know that one. well, outcome of that was, that in 3 measuring you can find an odd ball out of 3^0 + 3^1 + 3^2 = 13 balls.