## 27 marbles and a balancing scale

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AntonT
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### 27 marbles and a balancing scale

You are given 27 marbles - all identical looking. 26 are identical in mass, the 27th is slightly heavier than the rest. Only using a balancing scale (one that only shows which side is heavier) 3 times, how would you determine the heaviest ball?

Yakk
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3^3 = 27. QED.

skeptical scientist
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Nice solution, Yakk. I approve.
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Strilanc
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You are given 3^n marbles - all identical looking. 1 is slightly heavier than the rest. Only using a balancing scale (one that only shows which side is heavier) n times, how would you determine the heaviest ball?

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Drostie
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For people who have never seen the solution before, and want to know what it is:

Split your marbles into three groups A, B, and C. Measure A versus B. If the heavy marble is in A, then A>B. If the heavy marble is in B, then A<B. If the heavy marble is in C, then A=B. So one weighing will let you separate between 3 different options. More generally, if N is not divisible by 3, either leave C with one more marble if N ≡ 1 (mod 3), or one less marble if N ≡ 2 (mod 3). This will allow you to find the heavy marble in ceil( log3( N ) ) comparisons.

gmalivuk
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A fairly quick search (for "weighing marbles") would show that this has already been solved in a far more general form here.
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