What do you think of this recreational math problem?

Asked by LostInParadise (31907

) May 3rd, 2019

There are a few classic recreational math problems that ask to find a counterfeit coin using a balance scale, knowing that the weight of the counterfeit is different from the others. For example, determine in two weighings which of 9 coins is heavier than the others.

Here is my addition to these problems. The country of East Fenwick has four coins, of value of $1, $5, $25 and $100. They all have the same weight.

Someone walks into your office with four bags, each one containing coins of one of the denominations. You are told that higher valued coins have been counterfeited. The higher valued coins all have the same weight, but they are heavier than the lower valued coins. The person leaves abruptly without telling you where the division is between lower and higher valued coins.

Assuming that what you have been told is true, determine which of the coins are counterfeit in one weighing of the balance.

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2 Answers

I have heard of Grand Fenwick, famous for its wines and the victory in its war against the US.

Not familiar with East Fenwick, however.

elbanditoroso (33153

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Doesn’t look like there is much interest. My opinion is that the problem is okay, but takes to long to describe to be a really good recreational math problem. As to the solution, put the $1 and $25 coin on one pan and two $5 coins in the other. This will tell if just the $100 coin is counterfeit, or just the $100 and $25 coins are, or if the $100, $25 and $5 coins are all counterfeit.

LostInParadise (31907

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