Car Wheel Puzzle | Puzzles for Interview - Interview Preparation PDF Download

Introduction

Do you ever wonder how long your car tyres will last before wearing out completely? In this puzzle, we will find out the maximum distance a car can travel before needing a new tyre.

Problem Statement

A car has four tyres and one spare tyre. Each tyre can travel a maximum distance of 20000 miles before wearing off. What is the maximum distance the car can travel before you are forced to buy a new tyre? You are allowed to change tyres (using the spare tyre) an unlimited number of times.

Solution

To find the maximum distance the car can travel, we need to divide the lifetime of the spare tyre into four equal parts, which is 5000 miles. Then, we will swap the spare tyre with one of the four tyres at each completion of 5000 miles distance. Let's name the four tyres as A, B, C, and D, and the spare tyre as S.
1. 5000 miles:
Replace tyre A with the spare tyre S. The remaining distances for tyres A, B, C, D, and S are 15000, 15000, 15000, 15000, and 20000 miles, respectively.
2. 10000 miles:
Put tyre A back to its original position and replace tyre B with the spare tyre S. The remaining distances are now 15000, 10000, 10000, 10000, and 15000 miles, respectively.
3. 15000 miles:
Put tyre B back to its original position and replace tyre C with the spare tyre S. The remaining distances are now 10000, 10000, 5000, 5000, and 10000 miles, respectively.
4. 20000 miles:
Put tyre C back to its original position and replace tyre D with the spare tyre S. The remaining distances are now 5000, 5000, 5000, 0, and 5000 miles, respectively.
5. 25000 miles:
Every tyre is now worn out completely, and you need to buy new tyres for the car.

Conclusion

By using the spare tyre and swapping it with the four tyres at each completion of 5000 miles distance, we can find out the maximum distance a car can travel before needing a new tyre, which is 20000 miles x 4 = 80000 miles.