The riddle reads:
- There are 100 prisoners sentenced to life in prison.
- There’s a central living room with one light bulb which is initially off.
- No prisoner can see the light bulb from his or her cell.
- Every day, the warden picks a prisoner equally at random, and that prisoner visits the living room.
- While there, the prisoner can toggle the bulb if he or she wishes. The prisoner has the option of asserting that all 100 prisoners have been to the living room by now.
- If this assertion is false, all 100 prisoners are shot. “If it is indeed true, all prisoners are set free and inducted into MENSA, since the world could always use more smart people.
- Thus, the assertion should only be made if the prisoner is 100% certain of its validity.
- The prisoners are allowed to get together one night in the courtyard, to discuss a strategy. What plan should they come up with so that someone will make a correct assertion?”
Answer to the 100 Prisoners Light Switch Riddle
To solve this puzzle, the prisoners need to devise a strategy that ensures the assertion is made only when all prisoners have visited the living room. Here’s a detailed plan they can follow:
1. The prisoners agree on a system where one prisoner will be designated as the “counter” and the rest will be “switchers.”
2. Initially, the counter prisoner is chosen arbitrarily, and everyone else is a switcher. They can use any fair method to decide who becomes the first counter, such as drawing lots or choosing the eldest or youngest prisoner.
3. The counter’s role is to keep track of the number of switchers who have visited the living room. They will count by the state of the light bulb: on or off. Initially, the counter notes that the light bulb is off.
4. Each day, when a switcher is chosen to visit the living room, they will do the following: a. If the light bulb is off, they will toggle it on and increase the count of switchers by one. b. If the light bulb is already on, they will leave it unchanged and not increase the count.
5. After visiting the living room, each switcher will also toggle the light bulb off again, so that the next switcher can continue the count correctly.
The Next Steps
6. The counter will communicate the current count to the other prisoners during their nightly courtyard meeting. They can use a code system where each count corresponds to a specific number or pattern, making it easier to remember without arousing suspicion.
7. Once the counter determines that all 99 switchers have visited the living room (as they can see that the count is 99), they will know that they must also have visited. On the next day, the counter will assert that all 100 prisoners have been to the living room.
8. If the assertion is correct, all prisoners will be set free. If it is incorrect, they will all be shot, so the word should only be made when the counter is 100% certain of its validity.
9. If the counter is shot before making the assertion, the remaining switchers will continue the count until they reach 99, and the next counter will take over the role. This ensures that eventually, a counter will be able to make the correct assertion.
By implementing this strategy, the prisoners can guarantee that the assertion is only made when all prisoners have visited the living room, thereby maximizing their chances of survival and freedom.
Conclusion
The “100 Prisoners and the Light Bulb” puzzle demonstrates the power of collaboration, strategic thinking, and meticulous planning. By establishing a system where designated counters and switchers work together. The prisoners manage to keep track of each other’s visits to the central living room. If you like solving these kinds of Riddles please give them a go for fun.
Through their collective efforts, they overcome the randomness of the warden’s selection and succeed in asserting that all 100 prisoners have been to the room.
This puzzle serves as a reminder of the potential of human intellect and cooperation. These kinds of puzzles improve your logical skills and Intellectual skills. By showcasing how ingenuity can triumph even in the face of seemingly insurmountable odds.
By understanding and implementing their carefully devised plan. The prisoners pave the way for their freedom and leave us with a remarkable lesson in problem-solving and unity.