Color the heavier side blue and the lighter side yellow On your scale, there’s now a heavier and a lighter side.Color the four unweighed marbles green, because they are of normal weight.Outcome 2: After the initial weighing, the two sides don’t balance The same principle applies with the blue marbles, except in the final weighing, the heavier of the two is the oddball. If the two weigh the same, then the third, non-selected yellow marble is irregular. To identify the culprit, weigh two of the yellow marbles against each other. For example, if the three white marbles are lighter than the three green ones they’re weighed against, we can color the white marbles yellow. Based on this result, we know whether our irregular marble is lighter or heavier than normal. Sub-scenario 2: The two sides don’t weigh the same. To determine whether it’s lighter or heavier than normal, weigh it against a green marble. We also know the last marble is the irregular one. We now know that the three white marbles are normal, so we can color them green. Sub-scenario 1: The two sides weigh the same. Take three of the remaining four white marbles and weigh them against three of the eight green ones.Color the eight marbles on the scale green, because they are all of normal weight.Now, we break down the possible outcomes.Divide the 12 marbles into three groups of four.Setup: We start with 12 white marbles, because without weighing any of them, we have no information regarding their relative weight. Note that in the TED-ED video, “0”, “+”, and “-” are used in place of the green, blue, and yellow, respectively, but the principles outlined below still apply. To help us stay organized, we can create a key as follows: The hardest part about this problem is keeping track of the various scenarios. As promised in the video, I also want to provide a written solution.
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