Congratulations on tackling this classic puzzle! Let’s break it down step by step and uncover the logic behind the solution.
The Solution
This puzzle is a variation of the famous Josephus Problem, which involves identifying the safe position in a circle where people are eliminated in a set pattern. Here’s how to solve it:
Step 1: Understanding the Pattern
In this case:
- Starting with chair #1, every second chair is removed.
- This process continues around the circle until only one chair remains.
- The key is to recognize the pattern of elimination and calculate the safe position.
Step 2: Using the Formula
For a circle of people, the safe position can be calculated using:
Where:
- , and is the largest power of 2 less than or equal to .
Step 3: Applying the Formula
For :
- The largest power of 2 less than or equal to 100 is .
- Calculate .
- Substitute into the formula: .
Thus, the last remaining chair is #73.
Why Does This Work?
- The Josephus Problem follows a predictable pattern based on powers of 2.
- By subtracting the largest power of 2 from the total number of chairs, you determine how far the safe position is from the start of the circle.
Final Answer
The last chair standing is chair #73.
Well done if you figured this out! Ready for your next challenge? Keep exploring TQ for more brain-teasing puzzles. 😊