Brain Game: I'm So Tired


Tom owned an old Ford LTD that was in reasonably good shape for its age. He sold it on eBay, and worked out a deal with the buyer, who wanted to restore the car to its original glory. Tom would drive the car to the buyer's garage, some 1,800 miles away, where the new owner would buy Tom a hotel room for the night and spring for a plane ticket back home. The car was ready for the trip except for one thing: It lacked tires.

Tom's neighbor, Walt, had eight used tires that fit the LTD, but all of them were old and wouldn't make it very far. Each of the tires had enough tread to travel 1,200 miles, but he wouldn't trust them past that point. Of course, driving a gas-guzzler for such a long distance, Tom wanted to save as much money as possible by traveling light.

"I hate having to put four tires on the car and then carry four more in the trunk," Tom said.

"You don't have to take that many spares," Walt corrected.

What's the minimum number of spare tires Tom would have had to bring with him to safely complete the journey?

Here is the SOLUTION.


Tom could have made the trip with only TWO spares. Here's how:

He'd put four tires on the car, then drive the first 600 miles of his journey. At this point, he'd replace two of the car's tires (say, the back two) with the two spares, placing the two removed tires in the trunk.

He would travel another 600 miles of the trip, by which time the front tires would have reached their 1,200-mile limit and would need to be replaced. He'd remove those front tires, and replace them with the two from his trunk (which still have 600 good miles left on them). So with tires on the front and the back with 600 miles of tread left on them, he could then go the final 600 miles and complete his 1,800-mile trek.