A curious problem about an insidious tree stump that doubles the money

2024 Author: Malcolm Clapton | [email protected]. Last modified: 2023-12-17 03:44

Find out how much money was in the wallet of a naive peasant who really wanted to get rich.

Once a peasant met an unfamiliar old man in the forest. They started talking, the old man looked around the peasant and said:

- I know in this forest an amazing stump, which helps a lot in need.

- How does it help?

- You need to put a wallet under it, count to a hundred, and there will be twice as much money in it.

“I wish I could try this stump,” the peasant said dreamily.

“Pay me, and I'll show you the way,” the old man replied.

They began to bargain. The old man, having learned that the peasant did not have much money in his wallet, agreed that after each doubling, he would pay him only 1 ruble 20 kopecks. On that and decided.

The old man took the peasant into the depths of the forest, found an old stump among the bushes, took the wallet and thrust it between the roots. They counted to a hundred, the old man fumbled between the roots of the stump, took out a wallet and gave it to the owner.

The peasant opened his wallet and saw that the money had really doubled. As he had promised, he paid the old man 1 ruble 20 kopecks and asked him to once again shove his wallet under the magic tree stump.

They again counted to a hundred, and the money in the wallet again doubled. The old man received another 1 ruble 20 kopecks.

They did this experiment again, the peasant paid the old man again and found that there was not a single penny left in his wallet. The peasant had to go home with nothing.

As you might guess, the magic doubling of money is the work of a cunning old man who decided to cash in on a gullible peasant. He quietly slipped money into his wallet as he fumbled between the roots.

But the question is different: how much money was in the peasant's wallet before the ill-fated experiments with the tree stump? Try to answer!

This task must be solved from the end. If it is known that the peasant was left without money after the third payment to the old man, then immediately after the third doubling in his wallet there should have been exactly 1 ruble 20 kopecks. This means that until the last doubling, he had 60 kopecks left.

This amount ended up in the wallet after the second payment to the old man. To find out how much the peasant had before her, you need to add 1 ruble 20 kopecks to 60 kopecks. It turns out 1 ruble 80 kopecks.

Now you need to divide 1 ruble 80 kopecks by two to calculate how much money was in the wallet before the second doubling. It will turn out to be 90 kopecks. To this amount, you must again add the payment to the old man: 90 kopecks + 1 ruble 20 kopecks = 2 rubles 10 kopecks. So much was the peasant immediately after the first doubling before the payment to the old man.

To find the initial amount, you just need to divide 2 rubles 10 kopecks by two. It turns out 1 ruble 5 kopecks. That is how much the peasant had in his wallet before he met the old man.

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The problem is taken from the book of the Soviet mathematician and popularizer of science Yakov Perelman "".