Curious Contract
A visitor at a Motel makes a curious contract with the landlord. He wants to pay for his board and lodging by giving one link of a gold chain he possesses, on a daily basis. As the chain has 63 links, this would permit the visitor to stay for 63 days. That’s 63 cuts.
However, later in his room as the visitor prepares to sever the first link, he realizes that fewer cuts would mean less work. And, on reflection, comes to the conclusion that the number of links he actually would have to cut is far smaller than he had initially imagined. So what is the minimum number of links that he must cut to enable him to carry out his regular daily payment schedule?
However, later in his room as the visitor prepares to sever the first link, he realizes that fewer cuts would mean less work. And, on reflection, comes to the conclusion that the number of links he actually would have to cut is far smaller than he had initially imagined. So what is the minimum number of links that he must cut to enable him to carry out his regular daily payment schedule?
Labels: logic
posted by Rajesh Lal at
7:14 AM
3 Comments:
I believe that the visitor could carry out his daily payment schedule after making only 3 cuts.
He would cut the 33rd link, leaving him with a 32 link segment and a single broken link. Then on the remaining chain, he would cut the 17th link, leaving him with a 16 link segment and another broken link. Finally he would cut the 9th link of the remaining chain leaving him with an 8 link segment, and a 4 link segment, as well as one more single brokem link.
Now he would have 3 single broken links, and 4 other segments with lengths of 4, 8, 16, and 32 links.
Using the binary system, he could then trade lengths back and forth each day to pay hios bill.
For instance, on the fourth day, he would give the landlord the 4 link segment in exchange for the three broken links he had previously given him.
32 cuts
Anonymous got it. S/he ended up with 1,1,1,4,8,16 and 32 lengths.
You can now combine these to produce every number between 1 and 63.
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