Fake coins!!!

Number Theory Level 3

You have twelve coins. You know that one is fake. The only thing that distinguishes the fake coin from the real coins is that its weight is imperceptibly different. You have a perfectly balanced scale. The scale only tells you which side weighs more than the other side.

What is the smallest number of times you must use the scale in order to always find the fake coin?

Use only the twelve coins themselves and no others, no other weights, no cutting coins, no pencil marks on the scale. etc.

These are modern coins, so the fake coin is not necessarily lighter.

Presume the worst case scenario, and don't hope that you will pick the right coin on the first attempt.


The answer is 3.

Tanveen Dhingra by tanveen dhingra , 19, India

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1 solution

First you weigh half. So you would with 6 of the coins. Next, you weigh half of that. So you weigh 3. Next you weigh half. So you weigh the two because it works tell you is the remainin coin is fake or not.

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But after weighing for the first time, how would you know which side contains the fake coin? Remember that the fake coin can be lighter or heavier.

I dont think the answer is 3.

ikhlaas ishmael - 6 years, 6 months ago

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