This is a very interesting game to help you develop analytical skills in thinking through numerous and various possibilities and routes when trying to reach a goal or achieve an end result.
There are twelve coins, all look alike, and eleven of them weigh exactly the same. One of the twelve is slightly off weight, maybe a bit heavier, or a bit lighter in weight than any of the other eleven. You have one weigh scale, which only tells you which side is heavier (or lighter) when you have objects in the trays of the scale. The type of scale is shown below.
Scale: The type of coins (12 of them): etc.......
You are allowed to use the scale only 3 times, and on each weighing, the same number of coins must be on each tray of the scale. You may put any number of coins you choose into the tray, but the same number of other coins must be on the other tray.
Using the scale only 3 times, no more than that, how can you determine which coin out of the twelve is the coin that is not the same weight as each of the other eleven, and whether the odd weight coin is lighter or heavier than each of the other eleven. The other eleven are all exactly the same weight. All 12 coins look the same, and if you hold the coins in your hands, you cannot tell the weight of the coins or which one is slightly heavier or lighter. You can only tell which side of the tray goes up or down, depending upon whether the coins in the trays are lighter or heavier than the coins in the other tray. You also do not know where the odd weight coin is placed in the group of 12 coins; it is in there somewhere, but you do not know exactly where.
This problem is not easy to solve, because there are so many possibilities of which coins you pick to weigh, and what the result of the weighing tells you.
To help you get started, most people would first weigh six coins vs. six coins. If you do that, let's say the right side tray drops lower than the six coins on the left side. However, what does that information tell you? Well, the odd coin might be a heavier coin and it's one of the six on the right side tray, but...maybe that's not right. It could be that the odd coin is a lighter coin, and it is one of the six on the left side tray. So, you have used up one of the 3 weighings you are allowed, and you have not actually gained any new information. So, to start with one weighing of six coins vs. six coins is not the the way to start.
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