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Five apprentices are working for you, the village’s master blacksmith. After three days of work, you now have to pay them each a gold chain of 3 links. You have a gold chain of 15 links, which you can partition by cutting a link open, separating the chain, then welding it back. What is the minimum number of cuts you need to perform on this chain?

Hint

You can do it with less than 4 cuts.

Solution

3 cuts.

At first glance, you can make a single cut to separate out each chain of length 3, requiring you to make 4 cuts to create 5 chains of length 3. However, we can do better than that.

Notice that if you split a chain of length 7 at the middle link, you end up with 2 chains of length 3, with a single link that you can weld. Taking the chain of length 15, we can cut it at the 4th, 8th, and 12th link to produce 4 chains of length 3 and 3 individual links. We can weld these links back together to produce the 5th chain of length 3.

","rawContent","\nFive apprentices are working for you, the village’s master blacksmith. After three days of work, you now have to pay them each a gold chain of 3 links. You have a gold chain of 15 links, which you can partition by cutting a link open, separating the chain, then welding it back. What is the minimum number of cuts you need to perform on this chain?\n\n:::hint\nYou can do it with less than 4 cuts.\n:::\n\n:::solution\n3 cuts.\n\nAt first glance, you can make a single cut to separate out each chain of length 3, requiring you to make 4 cuts to create 5 chains of length 3. However, we can do better than that.\n\nNotice that if you split a chain of length 7 at the middle link, you end up with 2 chains of length 3, with a single link that you can weld. Taking the chain of length 15, we can cut it at the 4th, 8th, and 12th link to produce 4 chains of length 3 and 3 individual links. We can weld these links back together to produce the 5th chain of length 3.\n:::\n","dynamicBlocks",[],"inlineComponents",{},"actionData","errors"]

Chain Link 1

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Chain Link 2

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