The Rope Problem
Level
1
Suppose you are given a long rope. You fold the rope 3 times, with the 2 ends always with each other. Now, you cut the product at the middle.
How many parts of the rope will you get?
8
9
11
12
10
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1 solution
Suppose you have folded the rope 2 times, there will be the 2 ends on a side, 1 curved part on the same side, and 2 curved parts on the other side (the 2 ends of the rope are connected to the curved part, so there are 2 curved parts on the other side). So when you cut at the middle, there will be altogether 5 parts of the rope.
Note: Try picturing the image in your brain. If not, you can always draw on a piece of paper to help you visualise!
Now suppose you have folded the rope 3 times, but remember, when we folded the rope 2 times just now and cut at the middle, there were 4 lines of the rope being cut. So if we continued folding them and they were not cut yet, there will be 4 curved parts on a side. The 2 curved parts from the previous case are now brought to the other side by folding. So now when you cut at the middle, there will be:
The 2 ends on a side, 3 curved parts on the same side (1 from the previous case and 2 from the folding), and 4 curved parts on the other side Altogether, there are 2 + 3 + 4 = 9 parts of the rope.