Unlocking the Mystery: Which Cup Holds the Coin?
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Chapter 1: Understanding the Puzzle
Have you ever pondered which cup is most likely to conceal a coin? The probability here is not simply 1/3, but there's a deeper explanation at play.
This conundrum is reminiscent of the renowned Monty Hall problem, which highlights a surprising outcome: switching to the alternate option offers a 2/3 chance of success. Now, take a moment to evaluate the scenario presented in this coin under cup puzzle. Will the coin be hidden in the leftmost, middle, or rightmost cup? I encourage you to pause, grab some paper, and give it a shot before continuing with the solution!
Solution
To elucidate this puzzle, let’s employ a yellow cup to represent where the coin is located. The game initiates as follows:
According to the puzzle, the cups have been switched three times. Let's break down each switch:
- The rightmost cup was swapped with another one.
This cup could have been exchanged with either the middle or the leftmost cup. Note that the rightmost cup is marked red, indicating it does not contain the coin.
- The rightmost cup remained untouched during the second switch.
Here, the leftmost and middle cups swapped places. Thus, the situation remains unchanged, as the coin is still either in the leftmost or the middle cup.
- The final switch is crucial to our analysis, where the rightmost cup was swapped with another.
These four outcomes arise from the two scenarios presented in the previous step. The first and third outcomes show the rightmost cup switching with the middle cup, while the second and fourth outcomes involve it switching with the leftmost cup. Consequently, we find that in two out of the four scenarios, the yellow cup containing the coin is under the rightmost cup.
This indicates that the rightmost cup is indeed the most probable location for the coin!
What do you think about this conclusion? I would love to hear your thoughts in the comments below!
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