question involving math scales and logic
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You are hired by a king to examine 90 coins which are identical in appearance.
You are given an old scale (one where a platform or dish hangs from the end of a rod balanced in the middle) and you use the scale by placing objects on the scale’s two platforms to compare their weights.
In reality, only 89 of the coins are identical, the last one weighs a different amount than the other coins and is a counterfeit.
You must use the method that minimizes the number of times you use the scales and be able to explain how you were able to determine this minimum number of times (the algorithm you used).
If you can do so correctly, the king will grant you a great reward.
However, the scale is very valuable, old, and fragile, and it will break at some point if you weigh the coin more than the actual minimum amount of times.
If the scale breaks, you will be killed.
What is your solution to find the counterfeit coin in the least number of weighings and what is your best explanation?
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