Thanks to everyone who submitted answers to this week’s puzzle. This week’s GeekDad accolades go to Andy Grenier and Daniel Powell, who both sent in the correct answer nearly simultaneously. There also seemed to be some confusion as to the nature of the bling in the puzzle. Read the solution after the jump.
– SolutioYour intergalactic contact has arrived with his android enforcer to deliver the crates of alien tech you need to build your meta-wave wormhole generator. "I will deliver crates each cycle of your Earth day but I require currency at each time of delivery," he says. Your angel investors are not due to come through until seven days from now but you desperately need your parts to complete the generator or your investors will walk away.
You do have an old gold chain bracelet with seven links—the one that belonged to your grandmother who taught you all you know of sub-dimensional thermodynamics. It has extreme sentimental value. Thinking fast, you tell your contact, "I cannot give you the currency until seven Earth days. But here is a human adornment that is made of an Earth metal far more precious than any other anywhere in your star system. Each link of the chain is easily as valuable as the currency you require. You may hold this as collateral until your currency is here."
"Excellent. I will take the adornment."
"No," you say. "I will give you only a piece of the adornment that is the equivalent value of what is delivered. Today I will give you one link, tomorrow two links, the next day three, and so on until the last day when you may have all seven. At this time, I will have your total currency and you will return my bracelet."
Your contact agrees and the deal is struck but you must now cut the chain. You want to make as little damage as possible to your heirloom.
What is the fewest number of cuts you can make so your alien contact can hold the collateral he needs but no more?
Answer: One cut.
The cut must be made in a link which is third from the end (either end, it doesn’t matter). This one cut allows this link to detach itself from a set of two links, and a set of four links. Now you have one, two, and four links.
On day one your alien contact gets the cut link. On day two, he returns the cut link in exchange for the two joined links. On day three you give him the cut link again. On day four, he returns all links and is given the set of four. On day five you give him the cut link. On day six you exchange the two links for the one. On day seven he has all the links. You complete your invention. Your investors arrive with the cash. You avoid disintegration. Everyone is happy.
Admittedly, there was some confusion as to whether the bracelet in question was a single length of chain or a closed loop. The puzzle assumes a length of chain. Credit goes to those who submitted two cuts as the answer assuming it was a loop.