How to break into a math book

Tom did not specify who the person who entered Omar's mansion and killed Mr. Omar was. The lengthy letter he left actually only pointed out one problem: that is, in the information given by Holmes about Bill, Allen, Brian and West. Among the four suspects, he only saw one of them, and he thought that this person was either Alan or Bill.

Moreover, Tom said that only one of Bill and Allen had been to the Omar Mansion. As long as Tom's clue information was reliable enough, this proved that Bill and Allen could not appear at the same time.So now this clue is actually not enough for them to judge the murderer of Mr. Omar, they must continue to look for new information.

After leaving the bar, the three of them decided to take a look around the Omar Mansion.Although the scene has been cordoned off by the police, the surrounding streets and alleys may leave some clues.

The Omar mansion is very large and magnificently decorated, but at this time, because of a murder case, it is covered with a gloomy atmosphere, and the whole street looks lifeless.

The gate of Oma's mansion was cordoned off, and the three of Tu Hua bypassed the cordoned-off area and went directly to the street behind the mansion.There are only two windows on the wall behind the mansion, and the windows are very high and closed tightly. It seems that they have not been opened for a long time, and there is nothing unusual about them.

Just as the three of them were studying the terrain, someone behind them suddenly called to stop them.Tu Hua looked back and saw a middle-aged man in a police uniform, with a baton in his hand, rushing towards this side in a hurry.

The three of Tu Hua looked confused, only to hear the police officer ask: "What are you three doing here sneakily?"

"We're just here to investigate..."

Before they could explain, the police officer took out handcuffs and tied Tu Hua up first, with a fierce look on his face: "The three of you must be related to the case! Come back to the police station with me!"

Unexpectedly, the police in the game are so unreasonable. Tu Hua originally wanted to go to the police station to explain to the police, but who knew that the middle-aged police officer would directly take them into the prison and detain them.

Moreover, the prison where they were held was also very strange. Rather than saying that it was a prison cell, it might be better to say that it was a corridor blocked by iron bars.There were a total of five iron gates in front of them. The three of them were imprisoned at the innermost side, with walls without windows on three sides, and only five iron gates in front of them.

The police officer who imprisoned them seemed to directly identify them as criminals related to the case. After locking the five iron gates, he stood on the outermost side of the iron gates and said to the three viciously: "Don't try to escape, as long as you are on the innermost side If you leave the door for more than two and a half minutes, the alarm will sound, and all the police officers will rush to arrest the criminals who want to escape."

Tu Hua didn't understand what he meant for a moment, how could he arrest the three of them so well?Without interrogation or investigation, he was directly identified as a criminal?

Tu Hua was about to argue with the police, when Shen Siyi suddenly stopped him: "I think... this is a trigger task."

"It is impossible for the police to arrest us for no reason and put us in this strange prison. The passage he just ordered sounds more like the rules of the game. And... have you noticed this? What's the difference between the five gates?"

Tu Hua followed Shen Siyi's gaze, and only then did he discover the details that he had been ignoring.There is a red electronic screen on each of the five door locks. The display on the front of the screen seems to be some kind of time limit, while the beating numbers behind it are a countdown.

The time limit in front of the first gate is 1 minute and 45 seconds, the second gate is 1 minute and 10 seconds, the third gate is 2 minutes and 55 seconds, the fourth gate is 2 minutes and 20 seconds, and the fifth gate has the shortest time, 35 seconds. Second.

And at the next moment, the countdown behind the fifth door reset to zero, and then the fifth iron door opened with a "wow", and then closed again in an instant.

The three finally understood: "The time on these doors is actually a countdown to the automatic opening of the iron doors?"

沈思易分析道：“所以第一道门每隔1分45秒打开一次，第二道至第五道门分别间隔1分10秒、2分55秒、2分20秒和35秒打开一次，我们只要趁着每道门打开的瞬间溜出去，就可以逃出这座监牢。”

Sun Wei nodded, recalling what the police officer told them just now: "But do you still remember what the police officer said just now? As long as we leave the first door where we are now for more than 2 minutes and 30 seconds, An alarm will be triggered.”

Tu Hua frowned: "So... this level requires us to pass through these five doors within 2 minutes and 30 seconds?"

The three of them all knew that this level seemed to give them a way out, but in fact it was almost impossible to pass through the five doors within 2 minutes and 30 seconds.Because the opening time of the third door alone takes 5 minutes and 2 seconds, the five doors will not open at the same time, and there will be a waiting time between each door. They wait for all the doors to open in turn before they can go out.

Sun Wei squatted down and counted with his fingers on the ground: "First, we must wait for the first door to open. After the first iron door opens in 1 minute and 45 seconds, the second door with an interval of 1 minute and 10 seconds is already in our doorway. It was opened once during the waiting process, and when the first door opened, 35 seconds had passed for the second round of the countdown of the second door, that is to say, we had to wait another 35 seconds before the second door could open. Open."

"By the time we passed the second gate, 2 minutes and 20 seconds had passed, and we couldn't pass through the remaining three gates within 10 seconds."

Shen Siyi looked at the countdowns under each door and fell into thought: "Theoretically speaking, your calculation is correct, but since the police officers lock all the doors, the countdown has already started."

"So far, the fifth door has been opened four times, because the opening time of each door is different. As the number of door openings increases, the opening interval between each door will also change."

"It's not impossible to pass five doors within 2 minutes and 30 seconds."

After Shen Siyi's reminder, Tu Hua also felt that this seemingly unsolvable level seemed to have some clues.From the perspective of the first door and the second door alone, when the first door is opened for the first time, if you want to wait until the second door is opened, you need to wait for another 35 seconds; , that is, after two 2 minutes and 1 seconds, that is, after 45 minutes and 3 seconds, the second door will open at the same time as the first door.

That is to say, within 3 minutes and 30 seconds, the first door was opened 2 times in total, and the second door was opened 3 times in total. time overlap.If they want to pass through the first two doors in the shortest time, they only need to quickly pass through the first door and the second door when the two doors open at the same time at 3 minutes and 30 seconds after entering the prison.

In the same way, they only need to find out the time when the five doors open at the same time, and then they can find a way to leave the prison.

Shen Siyi's idea was a little more clear: "This is actually a mathematical calculation problem. First, let's observe the opening and closing times of these doors. They are all multiples of 35."

“假如我们以35秒为一个时间单位的话，第一道门开启的时间就是3个时间单位，第二道门为2个时间单位，剩下三道门分别为5、4、1个时间单位。”

“就先拿第一道门和第二道门来看，我们想要在最短的时间内通过这两扇门，需要等待的时间正巧是这两扇门开启时间的最小公倍数。也就是3和2的最小公倍数6，6个时间单位就是6×35秒=210秒=3分30秒。”沈思易分析道，“所以按照这个规律来分析，我们想要连续通过5道门，就需要等待3、2、5、4、1的最小公倍数，即60个时间单位。”

Tu Hua calculated that 60 time units are 60 35 seconds, that is to say, they need to wait for 35 minutes to pass through these five doors, and after 35 minutes, these five doors will open at the same time.But according to their observations just now, there is still a certain distance between the five doors, and the opening time of each door is very short, almost an instant, and the five doors will close at the same time.

So even if they calculated the time for the five doors to open at the same time, they still couldn't seem to find a solution, because they couldn't pass through quickly at the moment when all the doors opened at the same time.

Sun Wei also wondered: "There is no way for us to pass through the five doors after 35 minutes, that is, the moment when all the doors are opened at the same time. The distance from the first door to the fifth door is at least 200 meters. Run as fast as you can, I'm afraid you will be trapped in the middle when you pass through two gates."

Tu Hua was also confused: "And as long as we leave the first door for more than 2 minutes and 30 seconds, the alarm will be triggered. And 2 minutes and 30 seconds can contain up to 4 time units. If we wait for 35 After 2 minutes, I passed through 2 doors, and it will take 55 minutes and [-] seconds before the third door will open again, and the alarm has already sounded."

Shen Siyi shook his head: "There must be a solution to this problem, but we haven't thought of it yet..."

It seems that the opening and closing sequence of these five doors is very chaotic, but as long as the opening time of each door is fixed, there must be some law among them that can be obtained through calculation.

He stared closely at the five doors that opened in sequence in front of him, and suddenly found that after the first door was opened, the second and third doors were opened in sequence, with the same time interval between them, and this time ...which happens to be 35 seconds.

沈思易终于明白过来，只要找到每两扇门之间等待的时间规律，就可以在4个时间单位内通过这五扇门。他在狭窄的牢房里来回踱步，嘴里念念有词：“3、2、5、4、1……最小公倍数……最小公倍数……对了！倍数！”

He looked at Tu Hua and Sun Wei excitedly: "I know how we should pass through these five gates!"