/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 52 While three wise men are asleep ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 52

While three wise men are asleep under a tree a mischievous boy paints their foreheads red. Later they all wake up at the same time and all three start laughing. After several minutes suddenly one stops. Why did he stop?

Short Answer

Expert verified
Answer: One of the wise men stopped laughing because he deduced that his own forehead must also be painted red, based on the observations that the other two wise men didn't stop laughing and taking into account the possible scenarios.

Step by step solution

01

Initial Observations

Since all three wise men have their foreheads painted red, without any verbal communication, they can observe that the other two have red foreheads. They also know that there are three wise men, and thus begin to think about the possible scenarios.
02

Analyzing Scenario 1

In this scenario, let's assume that only one of the three wise men has a red-painted forehead. If this were true, the other two wise men would see one with a red forehead, and one without. The one not having any paint on his forehead would immediately know that he himself is not painted, and thus stop laughing. However, since all are laughing, this scenario cannot be true.
03

Analyzing Scenario 2

In this scenario, let's assume that two of the three wise men have red-painted foreheads. If this were true, the two with red foreheads would each see one other wise man with a red forehead, and one without. Now, the one without a red forehead should have stopped laughing in the first minute (as mentioned in Step 2), but he didn't. This would make both the wise men with red foreheads realize that their foreheads are also painted red. Consequently, they would stop laughing after the second minute. Again, since all are still laughing after several minutes, this scenario cannot be true.
04

Analyzing Scenario 3

In this scenario, all three wise men have red-painted foreheads. Each wise man sees two others with red foreheads. Since Scenario 2 (two wise men with red-painted foreheads) could not happen, everyone would deduce that all three must have red-painted foreheads. By realizing that their own foreheads must be painted red as well, one of them (it could be any one of them) stops laughing, putting an end to the situation. In conclusion, the wise man who stopped laughing did so because he deduced that his own forehead must also be painted red, based on the observations that the other two wise men didn't stop laughing and taking into account the possible scenarios.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Problem Solving Skills
The exercise about the wise men and red paint demonstrates essential problem-solving skills. Problem solving involves systematically working through challenges to find effective solutions. In this case, the wise men need to figure out why someone would stop laughing, given they all wake up to see each other with painted foreheads. They approach this by evaluating different scenarios. In problem solving:
  • You define the problem clearly. Here, the problem is understanding why everyone keeps laughing despite realizing there is something unusual.
  • You identify possible solutions, as the wise men do with the assumed scenarios.
  • You test these scenarios against what you observe. Each step involves deducing the consequences of their laughter continuing or stopping.
By iterating through possibilities, the wise men arrive at a solution that matches their observations. This stepwise approach is a powerful method for overcoming complex puzzles.
Critical Thinking Abilities
Critical thinking is at the heart of the exercise with the wise men. It involves analyzing and evaluating information thoughtfully to form a judgment. The wise men apply critical thinking by:
  • Observing the initial conditions, that every person laughing sees others with painted foreheads.
  • Breaking down the problem into manageable scenarios and questioning their validity.
  • Considering what they know and don't know at the outset, such as their own forehead's state.
This structured evaluation helps to eliminate impossible scenarios. It's important in critical thinking to not just accept things at face value but to dig deeper, question assumptions, and refine understanding until the most logical conclusion is reached. The exercise teaches to be patient and consider multiple angles before jumping to conclusions.
Deductive Reasoning Techniques
Deductive reasoning involves drawing logical conclusions based on premises that are generally assumed to be true. In the case of the wise men, they use deductive reasoning by:
  • Starting with the premise that all they see are two others with red foreheads.
  • Developing logical conclusions, such as if two have red foreheads, the scenarios where less than that would have acted differently.
  • Concluding from the continued laughter that their own foreheads must have paint too, because other scenarios don't fit the evidence.
This process ensures that they reach a conclusion based on logical evidence, not just guesswork. Deductive reasoning helps clear ambiguities in situations where multiple possibilities exist, allowing for rational action based on solid reasoning. Through this exercise, the technique teaches us to be meticulous in assessing evidence before deciding.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Four mathematicians have the following conversation: Alice: I am insane. Bob: I am pure. Charlie: I am applied. Dorothy: I am sane. Alice: Charlie is pure. Bob: Dorothy is insane. Charlie: Bob is applied. Dorothy: Charlie is sane. You are also given that: a) Pure mathematicians tell the truth about their beliefs. b) Applied mathematicians lie about their beliefs. c) Sane mathematicians' beliefs are correct. d) Insane mathematicians' beliefs are incorrect. Describe the four mathematicians.

Identify one current topic related to engineering or technology that has no single simple solution and write a brief paper discussing issues related to the topic.

A new school has exactly 1,000 lockers and exactly 1,000 students. On the first day of school, the students meet outside the building and agree on the following plan: the first student will enter the school and open all the lockers. The second student will then enter the school and close every locker with an even number \((2,4,6,8\), etc.). The third student will then reverse every third locker \((3,6,9,12\), etc.). That is if the locker is closed, he or she will open it; if it is open, he or she will close it. The fourth student will then reverse every fourth locker, and so on until all 1000 students in turn have entered the building and reversed the proper lockers. Which lockers will finally remain open?

You and seven of your friends have ordered a round pizza. You need to cut it into eight pieces and are only allowed to make three straight cuts. How can you do this?

Of three men, one man always tells the truth, one always tells lies, and one answers yes or no randomly. Each man knows which man is which. You may ask three yes/no questions to determine who is who. If you ask the same question to more than one person you must count it as a question used for each person asked. What three questions should you ask?
See all solutions

Recommended explanations on Physics Textbooks

Fundamentals of Physics

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Waves Physics

Read Explanation

Electrostatics

Read Explanation

Rotational Dynamics

Read Explanation

Energy Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.