Story
There was a millionaire who suddenly got lucky.
One day, on his way home, the millionaire met a stranger who was dressed very ordinary. He didn’t want to talk to the man, but the man took the initiative to talk to him. He seemed to know that the millionaire was rich, and before he could say a few words, he talked about a money exchange contract.
“Let’s make a contract.” The stranger said, “According to this contract, I will give you 100,000 yuan every day for a whole month, and you only need to give me one cent on the first day.,
“100,000 yuan? Only give you one cent?” The millionaire couldn’t believe his ears.
“Yes, one cent.” The stranger said affirmatively, “I will give you another 100,000 yuan according to the contract on the second day, and you give me two cents.
“So what about the future?” The millionaire became impatient.
“It will be like this from now on: I will pay you 100,000 yuan for the third time, and I will get 4 cents, 8 cents for the fourth time, and 16 cents for the fifth time. For a whole month, I will get twice as much money every day as the day before.”
The millionaire did not believe that there would be such a big fool in the world. He even suspected that the man was suffering from mental illness. But then he thought, as long as he could make more money, why bother about anything else! He asked anxiously:
“What will happen in the future?”
“There will be nothing in the future.” The stranger said, “Just you and I will strictly abide by this contract. I will bring you 100,000 yuan every morning, and you will pay me according to the contract until one month is up.”
“Let’s find a few people to witness and sign a formal contract! In order to avoid empty words and unpleasant things in the future.” The millionaire was afraid that the stranger would regret the contract once he woke up.
So, the two of them completed all the formalities. The millionaire returned home and was so happy that he couldn’t sleep all night. “Sometimes people get lucky.” He thought happily while lying on the bed. But he was also worried: Will that person really come? Could the money he sent be fake?
Early the next morning, the stranger really knocked on the door. He put 100,000 yuan in front of the millionaire.
The millionaire took the money with trembling hands, counted it twice, and checked it one by one to see if it was fake. When he was completely relieved, he gave his one cent to the stranger.
“I will send 100,000 yuan again at this time tomorrow, but don’t forget, please prepare two cents.” The stranger said and left.
“This is God’s will, which makes me lucky.” The millionaire kept muttering. The next day, the stranger brought money again and took away the two cents he deserved.
The millionaire took the second 100,000 yuan and thought: “How good it would be if there were more fools like this in the world, so that my life would be better…”
On the third day, the stranger brought 100,000 yuan and exchanged it for four cents.
On the fourth day, he exchanged the fourth 100,000 yuan for eight cents. On the fifth day, he exchanged 16 cents.
By the tenth day, the millionaire had received one million yuan, and the total amount he paid was only 10.23 yuan.
At this time, the greedy millionaire really regretted that the contract was only for one month and he could only get 300 yuan. Why didn’t he think of signing for two months, three months or even longer?
By the twentieth day, the millionaire had received two million yuan. The stranger still received very little, which is not difficult to calculate: 1+2+4+8+……+524288 =1048575 (cents), a total of a little more than 10,000 yuan, which is only 200th of the millionaire’s.
However, starting from the twentieth day, the millionaire found that his expenses were surging. The situation is:
When the millionaire received the 21st 100,000 yuan, he gave the stranger a little more than 10,000 yuan in person; when he received the 22nd 100,000 yuan, he gave the stranger more than 20,000 yuan; when he received the 27th 100,000 yuan, he gave the stranger more than 670,000 yuan.
The more terrifying scene is still in the last three days: when he received the 28th 100,000 yuan, he had to pay the stranger more than 1.34 million yuan in person; when he received the 29th 100,000 yuan, he had to pay the stranger more than 2.68 million yuan; when he received the 30th 100,000 yuan, he had to pay the stranger more than 5.36 million yuan in person!
As a result, while the millionaire received 3 million yuan in one month, he had to pay the stranger a total of 1+2+4+8+16+……+536870912=1073741823 (cents), which is about 11 million yuan.
The greedy millionaire only noticed that the price he paid was insignificant at first, and never expected that the number would become so amazing after doubling. He wanted to get a bargain, but suffered a big loss. The “lucky” millionaire went bankrupt completely!
Data analysis
Draw a picture to see the income and expenditure of the millionaire very intuitively.