Math: A rope is broken 3 folds and cut in the middle of the weight

Let the rope length be x, after folding n times, and the length of each rope is xn, then xn is equal to x divided by 2 to the n power.

Fold it n times in half, and there is 2 (n)+1

For example, if you fold it in half once, there are 2 1 + 1 = 3 segments.

Fold it in half twice, and there are 2 2 + 1 = 5 segments.

The answer to this question is: 9 paragraphs.

Think of it like this:

Fold it in half n times and cut it in the middle to divide the rope into 2 (n+1) segments.

In addition to the two small sections at both ends of the original rope, the rest of the small sections can be connected into two sections (due to the folding in half), and there are a total of: reserve number lift [2 (n+1)-2] 2+2=2 (n)+1

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Fold it n times in half, and there is 2 (n)+1

For example, if you fold it in half once, there are 2 1 + 1 = 3 segments.

Fold it in half twice, and there are 2 2 + 1 = 5 segments.

This question is: 9 paragraphs.

y is the number of segments x is the number of folds.

The equation is: y=2 to the power of x + 1

Fold in half 1 time for 3 sections.

Fold in half 2 times for 5 sections.

Fold in half 3 times for 9 sections.

Fold in half 4 times for 17 segments.

Fold in half 5 times for 33 segments and so on and so forth

9 sections, a rope is folded in half, cut from the middle, you can get 3 sections, 3 * 3 = 9

Fold in half 1 time, cut it in half for 2 roots, fold it in half 2 times, cut it in half for 4 roots from the middle (then 2 to the 2nd power) and fold it in half 3 times from the middle to 8 heels (then 2 to the 3rd power).

Through careful scrutiny, the pattern is discovered:

After folding it in half 5 times, it is cut from the middle to the (2 to the 5th power) root, and it is 32 roots!!

Here's how your teacher should solve it: Fold the rope in half and then fold it in half. So the rope becomes 6 layers, and by cutting it in the middle, it creates 12 endpoints, and plus the original two endpoints, you have 14 endpoints, and you should know the two endpoints to determine a piece of rope.14 2=7

But the number of times you fold in your problem doesn't turn out to be 7, because the fold is to bring two endpoints together, and folding five times becomes a 5th power layer of 2, and there are 64 endpoints from the middle break, 64 + 2 2 = 33

Do you understand?

Fold it in half twice, and after shearing it, it becomes 3 sticks.

Fold it in half three times and cut it into 5 sticks.

Fold it in half four times, and after shearing it, it becomes 9 sticks.

If n is folded in half several times, then it can be expressed algebraically: 2 to the power of (n-1) plus 1

Solution: A rope is folded into three equal sections, and then folded in half once and cut from the middle, a total of six sections can be cut.

After a rope is folded in half three times and cut from the middle, how many sections are cut in total?

A compound rope is first folded in half, then folded in half, and then cut from the middle after two folds, and this rope is cut into 5 sections.

Equation: 2 2+1. Fold twice, the number of folded segments is doubled to 2 2, and the +1 behind is the same as the tree planting principle. As shown in the figure below:

2×2+1=5

Fold twice, and the number of segments doubled to 2 2 each time

The +1 in the back is the same as the tree planting principle