This puzzle about a professional chicken farmer has stumped many people

Puzzle One

The professional chicken farmer

Professional chicken farmer Old Zhao one day discovered that egg production had dropped, and he suspected that his neighbor Zhou Er had stolen the eggs, so he came up with an idea. The next day, Zhou Er had just stolen the eggs and gone out the door when Old Zhao blocked his way, and Zhou Er retorted that they were fresh eggs laid by his own hens. Old Zhao said his eggs had marks on them, and Zhou Er did not believe it, so Old Zhao casually took out an egg and cracked it open with a "smack," and sure enough, every one had a mark, and Zhou Er was dumbfounded. Do you know what mark Old Zhao had put on the eggs?

Puzzle Two

The strange crime of passion

At night, in a dance hall full of bright lights and revelry, a man was slowly walking toward a woman, his face full of murderous intent.

The woman was a beautiful dancer.

The man had been the woman's boyfriend for many years, but had recently been ruthlessly abandoned by her. For money, the woman had thrown herself into the arms of a wealthy old man. To show her sincerity to the old wealthy man, the woman, in front of the wealthy man and everyone else in the dance hall, showed utter contempt for the man and even humiliated him.

The man decided to take revenge.

The man bought a gun and tested it, finding it indeed worked well, so one day he brought the gun to the dance hall, started a small fire in the restroom, and taking advantage of the chaos, went over to the woman, fired a shot at her heart, and quickly fled.

Unexpectedly, a few days later, he actually discovered that the woman was still alive. But he had clearly aimed at the woman's heart, so she should have been certain to die. Why was this?

Puzzle Three

The pie that solved the case

The friend of the famous French mathematician Goulard, Ruber, was murdered. Ruber was also a mathematician, and he had suffered severe injuries to his abdomen. When he died, in his hand he held only this one unfinished pie.

Upon investigation, no one had entered or left the apartment building on the day Ruber was murdered. Each floor of the apartment building had 15 rooms, with five floors in total, so checking them one by one would be very laborious.

Goulard said a few words to the police, and the police quickly found the murderer.

How did he help the police solve the case?

Answers

1. The professional chicken farmer

Answer: Old Zhao calculated that Zhou Er would come again to steal, so he put the good-for-nothing rotten eggs that could not hatch into chicks into the chicken house. Therefore, what Zhou Er stole were all rotten eggs, and rotten eggs could not possibly be freshly laid by hens.

2. The strange crime of passion

Answer: The woman was a dancer, and because her profession required it, in order to be more beautiful, she had breast augmentation, with silicone filling her chest, and this silicone just happened to block that fatal bullet.

3. The pie that solved the case

Answer: The English word for pie is pai, and pi

is generally calculated as 3.14. That pie hinted that the murderer lived in Room 14 on the 3rd floor. Investigation indeed confirmed this was so.