You have 8 identical-looking balls. One of them is slightly heavier than the rest
You have 8 identical-looking balls. One of them is slightly heavier than the rest. Using a balance scale (no weights, just tells you equal or which side is heavier), Aadi thinks finding the heavier ball needs at least 3 weighings. His sister says it can be done in just 2. Who is right?
Who do you think is right? Pick one.
The answer: His sister is right, it can be found in 2 weighings
Why
Aadi's guess likely comes from imagining testing balls one pair at a time, which really would need several rounds — but a balance scale gives more information per weighing than just 'is this one ball heavier than that one': weighing GROUPS against each other narrows things down much faster. Split the 8 balls into three groups: 3, 3, and 2. Weigh the two groups of 3 against each other. If one side is heavier, the heavy ball is among those 3 — weigh any 2 of those 3 against each other: if one side is heavier, that's the ball; if they balance, the one set aside is the heavy one. If the two groups of 3 balanced instead, the heavy ball is one of the 2 set aside — weigh those two directly against each other to find it. Test it: every single path through this method — heavier group found or not — uses exactly 2 weighings to land on one specific ball, never needing a third. His sister is right: 2 weighings are enough, because grouping balls together and comparing groups extracts far more information per weighing than testing one ball against another.
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