Required Mathematical Intelligence

Chapter 82 Selling Eggs

The great poet Benezhiktov is the author of the first anthology of mathematical brain-twisting topics in Russian.According to some "information" provided by the question itself, it is determined that the creation year of this question is 1869, but this year is not indicated in the manuscript.Let me introduce to readers a topic written by the poet in the form of a novel.The original question is called "Solutions to Weird Problems".

Once, a woman who was selling eggs sent her three daughters to the market to sell 90 eggs.She gave 10 eggs to the smartest eldest daughter, 30 eggs to the second daughter, and 50 eggs to the younger daughter, and said to them:

You discuss it first, and after you set the price, you must always stick to the same price without making any concessions.But I hope that the boss can use her wisdom, even if according to the price you have agreed in advance, she will get as much money from selling her 10 eggs as the second brother will sell her 30 eggs, and help the second The younger sister sold the 30 eggs for as much money as the third younger sister got from selling the 50 eggs.All three of you have to buy and sell at the same price as each other.

In addition, I hope that the price you sell will not be less than 10 cents per 10 eggs, and a total of 90 eggs will not be less than 90 cents, that is, 30 Ardennes.Now interrupt Benezhiktov so that the reader can think for himself: How did the three girls accomplish their task?

[Answer: The Benezhiktov story ends like this:

This topic is indeed very nerve-wracking.The three girls were walking and discussing on the way to the market.Later, the second girl and the third girl asked the elder sister for advice. The elder sister thought about it and said:
"Sisters, we used to sell ten eggs and ten eggs. This time we don't do that, we sell seven eggs and seven eggs. We order one for every seven eggs. The price, according to my mother's instructions, the three of us have to abide by it. Yes, the price will not be compromised! Every time I sell an Arden (3 points), what do you think?"

"That's too cheap." The second girl said.

"But when we have sold the seven eggs by the portion, we raise the price of the remaining eggs! I have noticed that there is no one selling eggs in the market today except the three of us, so there will be no Someone lowered our price. Then, as long as someone urgently needs the remaining precious goods and there are not many left, the price will naturally rise. We just want to earn back from the remaining eggs."

"So, how much are the remaining eggs sold for?"

"Eggs are sold for three Ardens. Give me the money, that's the price. Buyers who are waiting for the eggs to be cooked will pay this price."

"It's too expensive." It was the second girl who spoke again.

"Then what's the matter," the eldest sister replied, "Isn't our 'seven servings' of eggs sold too cheaply? The two are just offset."

Everyone agreed.

When they arrived at the market, the three sisters found a place to sit down and sell their eggs.Men and women who bought things saw that the eggs were so cheap, they all ran to the third girl, and her 50 chicken fleas were almost robbed in one go: she sold seven pieces of chicken fleas for seven pieces, and sold seven Ardennes. There is one egg left.The second girl had 30 eggs, and sold them to four customers seven by one, leaving two eggs in the basket, earning four Ardens.The eldest sister sold a share of seven eggs, earning an Arden, leaving three eggs.

At this time, a female chef came to the market, who was ordered by the housewife to purchase. Her task was to buy ten eggs.It turned out that the sons of the housewife especially liked fried eggs when they came back to visit relatives.The female chef was walking around the market, but the eggs were all sold out, and there were only six eggs left in the three egg stalls: one stall had only one, another had two, and a third had only three .Well buy them all!It is conceivable that the female chef first ran to the stall with three eggs, which was the stall of the eldest sister.The cook asked:

"How much do these three eggs cost?"

The man replied, "Three Ardennes to one."

"What's the matter with you? Are you mad?" said the cook.

The other said: "As you like, I won't sell it for less money. These are the few."

The female cook ran to the stall with only two eggs in the basket. "What's the price?"

"Three Ardens to one. The same price, the eggs are all sold out."

"How much do you sell your eggs for?" the female chef asked the third girl.

The man replied: "Three Ardennes."

There was nothing the cook could do.Had to buy the eggs. "Give me the rest of the eggs!"

So the cook paid the eldest girl nine ardennes for three of her eggs.In this way, together with the one Arden sold earlier, the eldest girl sold a total of ten Ardens.The second girl's two eggs got six Ardens, and together with the four Ardens who sold four eggs before, they got a total of ten Ardens.The third girl's remaining egg sold three Ardens, plus the seven Ardens that sold seven eggs before, and she got ten Ardens in total.

The three sisters returned home and each handed over ten Ardens to their mother. ]
(End of this chapter)