Lately, I’ve been asked several times for the solution to a problem circulating on the Internet. As I found it interesting, I’m going to try to explain it as simply as I can. I’ve even made some little drawings (you can click on any of the following images to enlarge them).
The statement is as follows:
The first and most important thing is to clarify that the euros do not evaporate. It may seem simple, well yes, but convince yourselves of that. Stop looking for the euro, it hasn’t gone anywhere. So, logically, something is wrong with the statement. The operations, sums and subtractions, are done correctly. The “trick” is that the calculation made at the end of the problem is not correct. It’s something subtle, which goes unnoticed, and then the confusion arises. So let’s quickly review the process.
At all times there are 100 euros in total. At the beginning, the father and the mother have 50 euros each. The child has nothing, and the shopkeeper has a T-shirt.
Now the parents lend him 50 euros each. The child has 100 euros, the shopkeeper has the T-shirt, and the parents have a 50-euro debt. I’ve drawn this as holes, meaning that each is owed 50 euros (this is the key to the problem).
The child buys the T-shirt. Now the child has 3 euros and a T-shirt, the shopkeeper has 97 euros, and each parent has a 50-euro debt.
Finally, the child gives one euro to each parent. The final situation is: one euro for each parent, one euro for the child, and 97 euros for the shopkeeper. Additionally, each parent has a 49-euro debt.
Obviously, at all times, 100 euros exist. The error is adding “holes” with “coins”. The 49 euros for each parent in the final situation are “debt euros”, that is, money the child owes them, so the calculation posed by the problem is incorrect.
An economist, or an accountant, would tell you that you were adding assets and liabilities. But since I’m not an economist, I’ll simply say that you’ve mixed apples and oranges.
