A rope is folded in half in 8 sections, cut from the middle, and there are a few formulas at the end

There are 257 in the end.

The formula is: fold in half n times, 2 to the n power + 1.

Solution process: For the first time, a rope is folded in half in half and cut from the middle; 2 primary square + 1 = 3 roots;

On the second time, a rope is folded in half in 4 sections and cut from the middle; 2 to the power of 2 + 1 = 5;

On the third time, a rope is folded in half for 8 sections and cut from the middle; 2 to the 3rd power + 1 = 9;

Fold it in half 8 times, and the answer is 2 to the 8th power + 1 = 257 roots.

So the formula is: fold n times in half, which is (2 to the n power + 1) root.

Fold in half n times, 2 to the n power + 1.

Solve it mathematically by induction.

For the first time, a rope is folded in half in half and cut from the middle; 2 primary square + 1 = 3 roots;

On the second time, a rope is folded in half in 4 sections and cut from the middle; 2 to the power of 2 + 1 = 5;

On the third time, a rope is folded in half for 8 sections and cut from the middle; 2 to the 3rd power + 1 = 9;

Fold it in half 8 times, and the answer is 2 to the 8th power + 1 = 257 roots.

So the formula is: fold n times in half, which is (2 to the n power + 1) root.

For such problems, mathematical induction can generally be used.

For the first time, a rope is folded in half in half and cut from the middle; 2 primary square + 1 = 3 roots;

On the second time, a rope is folded in half in 4 sections and cut from the middle; 2 to the power of 2 + 1 = 5;

On the third time, a rope is folded in half for 8 sections and cut from the middle; 2 to the 3rd power + 1 = 9;

If it is folded in half 8 times, the answer is 2 to the 8th power + 1 = 257 roots.

So the formula is: fold n times in half, which is (2 to the n power + 1) root.

Hope it helps!

m*2 n+1, m is the number of shears, n is the number of folds.

The number of segments in the process of folding in half from the middle is the nth power of 2, if it is folded in half once, it is divided into 2 segments, if it is folded in half and then folded twice, then the number of segments is 2 to the 2nd power = 4, if it is folded in half for the third time, it is 2 to the 3rd power = 8, cut it from the middle, it is equivalent to folding it in half again, so it is folded in half twice in this question, and cut it from the middle, that is, it is folded in half three times, so there are 8 segments.

The number of segments during the half-fold from the middle is 2 to the nth power. If you fold it in half once, divide it into two segments. If it is folded in half again, i.e. twice, the number of segments is a power of 2=4.

If it is folded in half for the third time, it is a power of 2=8. If it is cut in the middle, it is equivalent to folding it in half again. So, in this issue, it is folded in half twice.

If it is cut in the middle, it is folded in half three times, so there are 8 segments.

Fold a rope in half and then fold it in half. There are seven sections cut from the middle.

It is 4 paragraphs in total. A rope folded in half is two sections, and if it is folded and cut in half, it is four sections.

Fold it in half once, cut it from the middle and divide it into 3 sections, fold it in half twice, cut it from the middle and divide it into 5 sections.

Fold a rope in half twice, then cut it in the middle, making a total of 4 sections.

According to this rule, the number of capacitive segments obtained is different for each additional inner fold, as follows:

After folding in half twice, it can be cut from the middle, which can be cut into 4 sections, that is, 2 2 sections are folded in half three times and then cut from the middle, which can be cut into 8 sections, that is, 2 3 sections are folded in half four times and then cut from the middle, which can be cut into 16 sections, that is, 2 4 sections are folded in half n times and cut from the middle after being folded n times, and can be cut into 2 n sections.

One rope has two ports, two ropes have four ports...

Fold in half twice, so that the four rope segments overlap. Cut in the middle, add 8 new ports, plus the initial two, a total of 10.

So it's 5 pieces of rope.

If you are satisfied, please select the satisfactory answer.

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 in half 1 time, that is, 2+1=3 segments; Fold it in half 2 times, that is, 2+1=5 segments; Fold in half 3 times, that is, 2+1=9 segments; Fold it in half 4 times, that is, 2 of 4 times only Huai Fang + 1 = 17 segments; Fold it n times, which is 2 to the n power + 1 segment.

The most basic definition of power is: let a be a number, n be a positive integer, and the n power of a is represented as a, which represents the result of n a multiplication, such as 2 = 2 2 2 2 2 = 16. The definition of power can also be extended to the power of 0, to the power of minus, to the power of decimal numbers, to the power of irrational numbers, and even to the power of imaginary numbers.

Rope fold in half formula.

Fold it in half once and cut it from the middle and it is 3 sections.

Fold it in half twice and cut it from the middle, it is 5 sections.

Fold it in half three times, cut it from the middle, and it is 9 sections.

Fold it in half four times, cut it from the middle, and it is 17 sections.

Fold it in half n times, cut it from the middle, yes (2 to the nth power + 1).

Single-segment polyline problem.

Example 1: Fold a rope in half, fold it in half, and then fold it in half, and then cut it from the middle of the rope after folding, and ask how many small pieces of the rope has been cut?

Solution: We make the number of folds in half n, then the number of small segments cut into the end is 2n+1 segments, that is, 23+1=9 segments, so the answer is d.

Let's do one more question to reinforce this.

Example 2: A wire is cut from the middle after 5 folds in half, and ( ) is obtained?

Solve: In this problem, n=5, so we get 25+1=33 wires, choose b.

Multi-segment polyline problem.

In the rope folding problem, after folding the rope in half several times, some topics will cut a knife, and some topics will cut multiple knives, how to calculate the number of small segments cut at this time? Let's illustrate it with the following examples.

Example 3: Fold a rope in half, fold it in half, and then cut the rope in half into three sections, how many small pieces of rope is cut in total?

Solution: We make the number of folds in half be n, and the number of segments cut into m is m, then the number of small segments cut into is (m-1)2n+1 segments, that is, (3-1)22+=9 segments, choose d.

Fold it in half 3 times and cut it in the middle and cut it in 9 sections. First of all, it is 2 shares that are folded in half, 2 shares that are owed in half is 4 shares, and 8 shares that are folded in half 3 times. Only the two ends of the original rope are separated at its creases.

In this way, the 8 strands on one side are connected to the Begger macro every 2 strands, i.e. 8 2 4 segments. On the other side, there are 6 strands that are connected together every two strands, 6 2 3 sections, and the remaining 2 strands in front of the rope (the original ends of the rope are not connected together) are 2 strands. So 4 3 2 9 paragraphs.

Thank you. Handbook.

There are 8 sections of a rope folded in half 3 times, and the formula is as follows:Fold in half and hold the auspicious hand, divided into 2 sections; Fold it again, divided into: 2 2 4 segments; Fold the third time, divided into: 4 2 8 paragraphs.

Therefore, the feast is divided into 8 sections: 2 2 2 8 (segments).

Each segment is full-length: 1 (2 2 2) 1 8.

1. Dividend divisor = quotient.

2. Quotient = divisor.

3. Divisor quotient = dividend.

4. Divisor = (Dividend - Remainder) quotient.

5. Quotient = (number of excluded auctions - remainder) divisor.