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Imagine there are 100 light bulbs in a room, each controlled by its own switch. There are 100 people, each labeled with a unique number from 1 to 100. Each person will walk into the room and toggle the switches that correspond to the multiples of their own number. For example, the first person will toggle all the switches, while the second person will toggle every second switch. This continues until the 100th person toggles their own switch. At the end of this process, can you tell me how many bulbs will remain lit, and why?

**1. Problem-solving :**This question assesses your ability to analyze a complex and hypothetical situation and derive a logical solution.**2. Critical thinking :**Evaluates your capability to think deeply about a problem, understand its components, and come up with a reasoned answer.**3. Analytical skills :**This scenario requires you to break down the problem into smaller parts to understand the behavior of the switches and bulbs.**4. Attention to detail :**The correct answer depends on noticing patterns and details in the way the switches affect the state of the bulbs.

**1. Understanding problem complexity :**The interviewer wants to see if you can comprehend the complexity of the problem and still work towards a solution.**2. Evaluating logical reasoning :**This question tests your faculty for logical reasoning—an essential skill in technical fields.**3. Assessing intelligence :**Your answer can demonstrate your general cognitive ability and intelligence when faced with a novel problem.**4. Testing patience and persistence :**Complex problems can be frustrating. This question can gauge your patience and determination in reaching a conclusion.

**1. Consider the number of factors :**Reflect on how the number of factors a number has determines the number of times its corresponding bulb will be toggled.**2. Think about perfect squares :**Notice a pattern involving perfect squares that might explain which bulbs remain on.**3. Simulate smaller cases :**Try breaking down the process using a smaller number of bulbs and switches to observe the pattern that emerges.

Topics:

Problem Solving

Technical Skills

Roles:

Member Of Technical Staff

Companies:

Oracle

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