A variant of a puzzle in Raymond Smullyan’s The Riddle of Scheherazade: And Other Amazing Puzzles, Ancient and Modern
One day a customer brought into a jewellery
shop six chains, each of which had five links. He wanted the chains to be joined into one large circular chain. The jeweler said to the customer, “Each link I cut is a single piece of silver, and the total cost will be for the number of links I cut.” What is the minimum amount the customer had to pay?
Solution:
The usual answer is 6 pieces of silver, but the right answer is 5. If he takes one of the chains apart completely, he can then use the links from the taken apart chain to join the remaining 5 chains.
A variant of a puzzle in Raymond Smullyan’s The Riddle of Scheherazade: And Other Amazing Puzzles, Ancient and Modern
A thief entered a shop and decided to steal some diamonds. All of them were available to him, but he decided that would be too greedy. So he took half of what was available, and then he took one more. A second thief entered the shop and again took half of what was available, and then he took one more. Both the third and fourth thieves did the same thing: Each took half of the diamonds available when he or she was there, and then one more. A fifth thief entered the shop, but there were no more diamonds. How many diamonds were there originally?
Solution:
Since the fifth thief had none available, that means that the fourth thief had 2 available to him. And so the third had 6 available, the second had 14 available, and the first had 30 available. The answer is 30.
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