How To Solve The Seemingly Impossible Escape Logic Puzzle
TLDRIn this intriguing logic puzzle, Alice and Bob are imprisoned and can only escape by correctly guessing the total number of trees they can see, which is either 18 or 20. Alice sees 12 trees, and Bob sees 8, but they cannot communicate directly. The puzzle involves the prisoners using the process of elimination and the information gained from each other's responses to the daily question posed by the evil logician. Through a series of logical deductions based on their passes and answers, they eventually deduce the correct number of trees. On the fifth day, Alice confidently announces there are 20 trees, leading to their freedom. The video is an engaging exploration of logical reasoning and game theory, encouraging viewers to think critically and subscribe for more content on similar topics.
Takeaways
- 🔍 Alice and Bob are trapped and can see different numbers of trees, with Alice seeing 12 and Bob seeing 8, but neither can see the other's trees.
- 🤔 They are told there is a total of either 18 or 20 trees, and they must deduce the correct number to escape, with the risk of being imprisoned forever if they guess incorrectly.
- 📆 The evil logician asks them the same question daily, and their responses (or lack thereof) convey information to each other.
- 🙅♀️ Alice initially passes because she cannot determine the total, as she does not see enough trees to confirm 18 or 20.
- 📉 Bob also passes on the first day, which tells Alice that he doesn't see a number of trees that would allow him to conclude there are 18 total.
- 🔁 Each day's passes and answers build upon the information from the previous day, allowing them to narrow down the possibilities.
- 🔢 By the fourth day, Alice knows Bob sees at least six trees, and Bob knows Alice sees at most 12 trees.
- 💡 On the fifth day, Alice realizes that with her seeing 12 trees and Bob seeing at least eight, the only possibility is 20 trees in total.
- 🏁 Alice correctly answers that there are 20 trees, leading to their escape.
- 🧠 The puzzle demonstrates the power of logical reasoning and the importance of paying attention to details and the implications of each other's actions.
- 📚 The video encourages viewers to engage with math and game theory, and to follow the presenter on social media for more content.
Q & A
What is the main challenge faced by Alice and Bob in the riddle?
-Alice and Bob are trapped in cells and can only see a certain number of trees each. They must determine the total number of trees they can see without communicating directly with each other and with limited information.
How many trees can Alice see from her cell?
-Alice can see exactly 12 trees from her cell.
How many trees can Bob see from his cell?
-Bob can see exactly 8 trees from his cell.
What happens if Alice or Bob guesses incorrectly about the total number of trees?
-If either Alice or Bob guesses incorrectly without knowing the correct answer, they will both be imprisoned forever.
What happens if they both pass on their guesses?
-If both Alice and Bob pass on their guesses, the process repeats the next day with the logician asking the same question.
How does the passing of one person convey information to the other?
-The act of passing on a guess indicates that the person does not have enough information to determine the total number of trees, which in turn provides the other person with a clue about the range of possible numbers.
On which day does Alice finally know the correct answer to the logician's question?
-Alice knows the correct answer on the fifth day.
What is the significance of the fact that no tree is seen by both Alice and Bob?
-This fact ensures that each person has unique information about the total number of trees, which is crucial for the logic puzzle to work.
How does the logician's question change over time?
-The logician's question does not change; it remains the same each day, asking whether there are 18 or 20 trees in total. However, the information conveyed through passing or guessing evolves over time.
What is the key to Alice and Bob's eventual escape?
-The key to their escape is their ability to logically deduce information from each other's passing and the rules of the game, leading Alice to the correct answer on the fifth day.
What does this riddle illustrate about logical reasoning and communication?
-This riddle illustrates that even with limited direct communication, logical reasoning can lead to the transmission of meaningful information and the solving of complex problems.
How does the process of elimination work in this riddle?
-The process of elimination works by Alice and Bob using the fact that the other has passed to deduce what they cannot see, thus narrowing down the possibilities for the total number of trees.
Outlines
🔍 The Logic Puzzle: Alice and Bob's Dilemma
This paragraph introduces a logic puzzle where Alice and Bob are trapped and must use deductive reasoning to escape. They each can see a different number of trees, with Alice seeing 12 and Bob seeing 8, but no tree is visible to both. They don't know the other's count but are informed that together they can see all the trees in the prison. The evil logician gives them a chance to answer whether there are 18 or 20 trees in total. Correctly identifying the number sets them free, while an incorrect guess results in perpetual imprisonment. The catch is that they cannot communicate directly but must use the logician's questioning to deduce the correct answer. The paragraph sets up the problem and invites viewers to consider if Alice and Bob can use the rules of the game to their advantage and escape with certainty.
📚 Day-by-Day Deduction: The Path to Freedom
The second paragraph details the step-by-step logical process that Alice and Bob use to eventually deduce the correct number of trees. Starting from day one, each person's inability to answer the logician's question provides incremental information to the other. By passing on their chance to guess, they communicate the maximum number of trees they can see. This iterative process continues over several days, with each passing reducing the range of possible tree counts. On day five, Alice, knowing she sees 12 trees and that Bob sees at least 8, concludes that the total must be 20 trees, not 18, as 8 + 12 would not sum up to 18. She confidently announces there are 20 trees, which is correct, leading to their release. The paragraph concludes with a prompt for viewers to consider if they solved the puzzle and an invitation to engage with the content creator's social media and books.
Mindmap
Keywords
💡Logic Puzzle
💡Absolute Precision
💡Prison
💡Trees
💡Communication
💡Passing
💡Guessing
💡Game Theory
💡
💡Information Conveyance
💡Days
💡Freedom
Highlights
Alice and Bob are trapped and can see a different number of trees, but no tree is seen by both.
They are asked if there are 18 or 20 trees in total, but must pass if unsure.
If they guess incorrectly, they are imprisoned forever. If correct, they are set free.
Alice sees 12 trees, Bob sees 8, and they cannot communicate directly.
Each day they pass or answer, and their responses convey information to each other.
On Day 1, Alice passes, conveying she doesn't see 19 or 20 trees.
Bob also passes, conveying he doesn't see 0 or 1 trees, knowing Alice sees at most 18.
By Day 2, Alice knows Bob sees at least 2 trees, and Bob knows Alice sees at most 16.
If Bob saw 2 or 3 trees, he could conclude there are 18 trees, but he sees 8.
Bob's pass on Day 2 conveys to Alice he must see at least 4 trees.
On Day 3, if Alice saw 15 or 16 trees, she could conclude there are 20 trees.
But since Alice sees 12, she passes, and Bob deduces she sees at most 14 trees.
If Bob saw 4 or 5 trees, knowing Alice's max of 14, he could conclude there are 18 trees.
Bob's pass on Day 3 conveys he sees at least 6 trees to Alice.
On Day 4, if Alice saw 13 or 14 trees, knowing Bob sees at least 6, she could conclude 20 trees.
But since Alice sees 12, she passes, and Bob deduces she sees at most 12 trees.
If Bob saw 6 or 7 trees, knowing Alice's max of 12, he could conclude there are 18 trees.
Bob's pass on Day 4 conveys he sees at least 8 trees to Alice.
On Day 5, Alice deduces there must be 20 trees, as she sees 12 and Bob sees at least 8.
Alice correctly answers 20 trees, and they are both set free.
Transcripts
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