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Hello everyone, recently I discovered this puzzle and it’s too challenging for me I couldn’t solve it. If anyone knows the answer, I would really appreciate it if you can help me out here, thank you.

The puzzle :

You and another 100 prisoners are being locked up by a tricky warden. One day the warden comes to you and say: “I will give you a challenge, if you can pass the challenge then all 101 prisoners will be set free. There is a room which has 2 lightbulbs, one is yellow and one is green. Each lightbulb is controlled by an independent switch, so a prisoner can toggle whichever lightbulb they want on or off.

Everyday I will call up one of the 100 prisoners randomly into the room and let him toggle the switches. To ensure fairness, I will use a random number generator to call up the prisoner, but it doesn’t guarantee every prisoner will visit the room an equal number of times. And I will continue to do this everyday forever, for as long as it takes for them to solve my puzzle.

I won’t call you into the room, no. Your task is to devise a strategy for those 100 prisoners to follow. You must write it down onto a piece of paper and I will print 100 copies of it and give every prisoner a copy. So everyone must follow an exact same strategy with no variation whatsoever. That means you cannot elect a specific person to count the lightbulb, or give different instructions to different prisoners. Also, the prisoners cannot communicate with each other in any way.

At any time, a prisoner can declare that all 100 prisoners have already visited the room. And if he’s right, all of you will go free, but if he’s wrong, I will execute you all. What strategy can you devise to guarantee the freedom of all prisoners?

Hello Puzzle, I would like to test you with this famous paradox. Please try to solve it yourself and don’t look it up on the web.

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A rabbit and a tortoise decides to race. To keep things fair, the rabbit gives the tortoise a head start of say, 500 meters. When the race begins, the rabbit starts running at a speed much faster than the tortoise, so that by the time he has reached the 500-meter mark, the tortoise has only walked 50 meters further than him. But by the time rabbit has reached the 550-meter mark, the tortoise has walked another 5 meters. And by the time he has reached the 555-meter mark, the tortoise has walked another 0.5 meters, and so on. This deduction process can continue again and again over an infinite number of times while still remain true, there is no end to this chain process.

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Apparently, this seems to prove that the rabbit can never overtake the tortoise, whenever he reaches somewhere the tortoise has been, he will always still have some distance left to catch up. But in reality, we know the rabbit will overtake the tortoise. So now I ask you this : how to crack this paradox and defeat the false logic? I’m waiting for your answer.

You wake up in the morning. The paint is peeling, the curtains are gone, and the water is boiling. Which problem do you deal with first?