Car and Wheel Puzzle

Puzzle on Car and Wheel

In the car and wheel puzzle, a car consists of 4 tyres and 1 extra tyre. The maximum distance traveled by each tyre is 20000 miles before wearing off.
Rules – You have the freedom to change the tyres (including the spare tyre) an unlimited number of times.
Objective – What is the maximum distance the car can travel before you have no other option rather than to buy a new tyre?

Solution of the Puzzle

Let’s call the four tyres A, B, C, and D, and the spare tyre S.

Divide the spare tire’s lifetime into four equal parts, i.e. 5000 miles, then replace it out every 5000 miles.

1. 5000-kilo meters: Substitute S for A.
2. 15000, 15000, 15000, 15000, 15000, and 20000 km are the remaining distances (A, B, C, D, S).
3. 10000 kilometers: Replace B with S and return A to its original position.
4. 15000, 10000, 10000, 10000, and 15000 km are the remaining distances of (A, B, C, D, S)
5. 15000 km: Replace C with S and return B to its original location.
6. 10000, 10000, 5000, 5000, 10000 are the remaining distances of (A, B, C, D, S)
7. 20000 km: Replace D with S and return C to its original location.
8. 5000, 5000, 5000, 0, 5000 are the remaining distances (A, B, C, D, S)
9. 25000-kilo meters: Every tyre is now fully worn out.

Hence, in this way, we can achieve the given objective.

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