12. (2 points) [Puzzle] Assume that you have 8 identical-looking coins and a two

Question

12. (2 points) [Puzzle] Assume that you have 8 identical-looking coins and a two-pan balance scale with no weights. One of the coins is fake, but it is not known whether it is lighter or heavier than the real 7 coins. Describe your idea to determine in the minimum number of weighings whether the fake coin is lighter or heavier than the others. Present the minimum number of weighings and your answer clearly. In the problem, remember that I do not ask you to find the fake coin among 8 coins using the scale. You don’t need to find out which coin is fake. The question is that you should be able to identify whether the fake coin is heavier or lighter than the real coins.

12. (2 points) [Puzzle] Assume that you have 8 identical-looking coins and a two-pan balance scale with no weights. One of the coins is fake, but it is not known whether it is lighter or heavier than the real 7 coins. Describe your idea to determine in the minimum number of weighings whether the fake coin is lighter or heavier than the others. Present the minimum number oif weighings and your answer clearly. In the problem, remember that I do not ask you to find the fake coin among 8 coins using the scale. You don't need to find out which coin is fake. The question is that you should be able to identify whether the fake coin is heavier or lighter than the real coins.

Explanation / Answer

Given we have 8 identical looking coin. We need to figure out if the odd coin is heavier or lighter than other coins.

If we weight 4 coins on one balance and 4 coins on the other balance, we will see that one set is heavier than the other.

Now, let's assue that the fake coin is heavier (51gm) than the other coins.

Let's assume the weights are

So, set1 contains 50 50 50 51

set2 cointains 50 50 50 50

Let's take the lighter set of coins. If our assumption is correct , splitting set2 should weight equal on the pan. Since all are 50 each.

If that was not correct, that means,

set1 contains 50 50 50 50

set2 contains 50 50 50 49

If fake coin is lighter, splitting the set2 should produce imbalance when weighed on the pan.

So, ans is 2 weighings.

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