/*! 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 6 Two rooms are connected by a hal... [FREE SOLUTION] | 91Ó°ÊÓ

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Two rooms are connected by a hallway that has a bend in it so that it is impossible to see one room while standing in the other. One of the rooms has three light switches. You are told that exactly one of the switches turns on a light in the other room, and the other two are not connected to any lights. What is the fewest number of times you would have to walk to the other room to figure out which switch turns on the light? And the follow-up question is: Why is the answer to the preceding question "one"? (Look out: This question uses properties of real lights as well as logic.)

Short Answer

Expert verified
One trip is needed; use light and thermal properties of bulbs to identify the switch.

Step by step solution

01

Understand the Problem

We have a selection of three switches, but only one is connected to a light in another room. The hallway between the rooms prevents direct visibility of the light while standing by the switches.
02

Develop a Strategy

To minimize trips, we need to use the properties of a light bulb: it emits light when on, and it generates heat when it's been on. This can help identify the correct switch with just one trip.
03

Test the First Switch

Turn on the first switch and wait for a few minutes. This will allow the connected bulb, if any, to heat up.
04

Turn Off the First Switch and Test the Second Switch

After waiting, turn off the first switch and turn on the second switch. Then, immediately walk to the other room.
05

Assess the Situation in the Room

Upon reaching the other room, observe the light: 1. If the bulb is on, the second switch is correct. 2. If the bulb is off but warm, the first switch is correct. 3. If the bulb is off and cold, the third switch is correct.

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Key Concepts

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

Logic Puzzles
Logic puzzles challenge our reasoning abilities by presenting problems that require using deductive and often lateral thinking. In the exercise provided, the problem engages us with the configuration of light switches and the mystery of discovering which switch controls the light in the adjacent room.

The solution requires out-of-the-box thinking. Instead of randomly flipping switches and making multiple trips between rooms, the trick is to use a bit of logic that involves understanding not only how the switches work but also the physical properties of the light bulb.

Here's the clever part: light bulbs give off heat when they have been turned on. By using this property, you can create a plan that reduces trips. Turn on the first switch, wait for a while, then turn it off and turn on the second switch before going to check the bulb. In this setup, each outcome tells us something unique: the current warmth of the bulb or if it is lit leads directly to the identification of the correct switch. This example shows how logic puzzles often require understanding beyond the immediately visible factors, encouraging creative problem solving.
Critical Thinking
Critical thinking involves analyzing facts to form a judgment. It's about being actively engaged with information and problem solving rather than passively receiving it.

In this particular logic puzzle, critical thinking comes into play as you must consider different strategies to solve the problem effectively. The challenge is not only technical but also strategic. It requires understanding the underlying properties of the elements involved—the switches and the light bulb—rather than solely focusing on the visible information.

As you approach the problem, you need to weigh your options and predict possible outcomes of different actions. You ask, "What if I leave this switch on for some time?" or "How can I discern between the switches with minimal effort?" This kind of thinking is crucial because it helps to reach solutions with fewer efforts and resources. Adopting a systematic approach, like the proposed solution here, ensures that each action is purposeful and leads you closer to the answer.
  • Analyze the situation
  • Explore different angles
  • Devise clear and tested strategies
By employing critical thinking, you can tackle the task efficiently and effectively.
Scientific Method
The scientific method is a structured approach to understanding the world through observation, hypothesis formulation, experimentation, and analysis. Our puzzle exercise is a brilliant example of applying a simplified version of the scientific method to everyday problems.

First, you start with an observation: you have three switches, and only one activates a light in another room. The task is akin to forming a hypothesis about which switch affects the light. You then design an experiment, like turning on one switch to see its effect.

In the proposed solution, turning on the first switch and waiting is your experimental phase where you're testing a part of your broader hypothesis—does this switch affect the light, and how can I measure it through light and heat? This leads to your analysis when you enter the room and check which conditions hold true.

The approach illustrates applying a scientific mindset in logical puzzles:
  • Formulating a hypothesis: Imagine possible outcomes for each switch.
  • Designing an experiment: Adjust switches and observe conditions.
  • Analyzing results: Light being on or off, bulb warmth.
This process ensures a systematic way to reach the correct solution efficiently.

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Most popular questions from this chapter

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