You have 12 identical-looking balls and a balance scale. One ball is a different weight (heavier or lighter). You have only three weighings to determine which ball is different and whether it is heavier or lighter.
Common Wrong Answers
“Weigh all 12 balls against each other in pairs.”
This approach would require more than three weighings, as you would need to weigh multiple pairs to determine the odd ball, making it impossible to identify the different ball within the given constraints.
“Weigh 6 balls against 6 balls.”
While this is a good initial step, it doesn't break down the problem effectively for the next steps. You can't isolate which of the 6 balls is different in only two more weighings after this, as it leaves too many possibilities.
“Use a single weighing to determine the heaviest ball and assume it's the odd one.”
This method ignores the possibility that the odd ball could be lighter. Additionally, a single weighing won't provide enough information to conclusively identify the odd ball or its weight difference.
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