Fold a rope in half 50 times, cut it in the middle, and ask how many pieces the rope has been cut

Answer: 2 to the 50th power plus 1

Hello, this question Olympiad teacher has talked about, hehe.

In fact, the simplest and most intuitive method is the drawing method.

Just draw a line on the paper.

After the first fold, draw a line similar to a greater than sign">"At this time, if it is cut, it is 3 sections.

Draw a diagram of folding a second time, similar to"m"Horizontally, if it is cut at this time, it is 5 sections.

Fold it a third time, similar to joining it together"mm"Horizontally, if it is cut at this time, it is 9 sections.

Break it down: 1st fold and cut: 3 segments both:

2 to the 1st power plus 1 2nd fold and shear: 5 segments both: 2 to the 2nd power plus 1 3rd fold and shear:

Paragraph 9 both: 2 to the 3rd power plus 1 and so on, the 50th fold and cut: both:

2 to the 50th power plus 1 so that it is easy to solve and will not waste your time too much, I hope you can understand.

Friend, you are very studious. Admiration.

2 to the 49th power * 2 + 1 = 2 has 50 power + 1 (because the beginning of the cut has two heads together, after the cut is two, the rest of the cut is 1 section).

The number of segments on the left is 2, 2+1, 2+1+2, 2+1+2+4, ,..

That is, the number of segments on the left is: 2+[1-2 (n-1)] (1-2) and the number of segments on the right is 1, 2, 4,..

That is, the number of segments on the right is: 2 (n-1).

So the number of segments on the left and on the right is: 2 n+1

The answer is: 2 50+1 paragraphs.

2 to the 49th power. Because the fold for the first time is 1

So a rope is folded in half 50 times, cut from the middle, and the rope is cut into 562949953421312 sections.

Eldest brother. I'm half dead.!~

1 time 2 paragraphs. 2 times 4 paragraphs.

50 times is 50 squared.

The answer is: nine pieces of rope. Analysis: A rope is folded in half three times for a total of eight sections, and after being cut from it, the two are connected into seven sections of rope of the same length.

What remained were two short pieces of rope of the same length, half the length of the seven.

After folding it in half three times and cutting it, it is equivalent to cutting the rope 8 times (2 2 2), and 8 times is nine sections of rope.

1 2x2 2=8 (segment).

8 2 = 16 (segment).

A: A total of 16 ropes were cut.

This topic can be divided into two parts to understand, first, a rope is folded in half four times, how many strands do you become? Easy to know 1*2 4=16 shares.

As soon as it is cut upside down, there are 16 more broken ends in this rope, plus the first two heads, a total of eighteen heads, and it becomes a rope that starts at one end and ends at the other end with a total of 18 points (including the head and tail). Easy to know 17 paragraphs.

Calculated according to the end of the rope, no matter how many times you fold it in half, you will be able to do it.

A rope folded in half 4 times is 2 to the 4th power, 16 sections of rope overlap, cut in the middle, forming 32 endpoints, plus the original 2 ends of the rope before, a total of 34, 34 2 is equal to 17, so 17 sections.

The rope is 16 segments.

One fold and two sections. Two folds and four sections.

Three folds and eight sections. Four-fold sixteen paragraphs.

And so on.

After folding a rope in half four times, cut it from the middle. This rope is made up of several sections.

17. The formula for the disconnection term an=2 n+1, n represents the number of folds.

Fold in half and cut it once, 3 sections; Fold in half twice and cut in 5 sections, fold in half four times, 17 sections ......

It should be 16 paragraphs, and this is the answer process of this question.

This question is a fraction of the original total length after the test is folded in half. Now after the test is folded in half three times and then cut from the middle, in fact, it is required that the length after folding in half four times is a fraction of the original. Experimentally, the length of the four folds is one-sixteenth of the original total length.

Turn 1 16 into a percentage. That is, after folding in half three times, cut the shortest section from the middle, which is the original total length.

For these three times, a rope becomes 8 overlapping, then cut from the middle, the shortest section is the original 1 16, and the longest section is the original 1 8The shortest segment is the longest segment of 1 16 1 8 = 1 2

In fact, in this question, it has nothing to do with how many folds, you can give it a try. Fold once, the shortest is the original 1 4, the longest segment is the original 1 2, the shortest and longest = 1 2;The rest is similar.

Solution: A rope is folded in half three times in a row, 8 sections are double, and a total of 18 heads are cut from the middle, that is, 9 ropes, 7 of which each account for 1 8 of the total rope, and two short ones that each account for 1 16 of the total rope.

So the shortest is 1 16 (1 8) = 1 2 = 50% of the longest segment

That is, the shortest segment is 50% of the longest segment

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

Answer: 2 to the 50th power plus 1

In fact, the simplest and most intuitive method is to draw a picture.

Just draw a line on the paper.

After the first fold, draw a line similar to a greater than sign">"At this time, if it is cut, it is 3 sections.

Draw a diagram of folding a second time, similar to"m"Staring at the horizontal loss, if it is cut at this time, it is 5 paragraphs.

Fold it a third time, similar to joining it together"mm"Horizontally, if it is cut at this time, it is 9 sections.

Break it down: 1st fold and cut: 3 segments both:

2 to the 1st power plus 1 2nd fold and shear: 5 segments both: 2 to the 2nd power plus 1 3rd fold and shear:

Paragraph 9 both: 2 to the 3rd power plus 1 and so on, the 50th shout is folded and cut off: both:

2 to the 50th power plus 1 so it's easy to solve and won't waste your time too much, friend, you're good at learning. Chin Zheng admired.

4 paragraphs. After a rope is folded in half and slowly folded twice, cut from the middle, there are 4 sections, because the first time a line is folded in half is multiplied by two, and then which is folded in half and a punch orange is 2 times 2, and the result is 4. It's a mental arithmetic problem.

Q: How many sections can a rope be cut from the center after half of it has been cut 5 times?

a: After counting the rope in half once, two line segments can be obtained; Half of the two times, four line segments can be closed; After half three times, eight line segments can be obtained; After half of the four times, sixteen line segments can be obtained; After half of the five times, you can get thirty-two line segments. Thus, after half of the five times, a rope can be cut from the center into 32 sections.

q: 181.How many 8k are there?

A: The implication is 181,800, or one hundred and eighty thousand eight thousand. The "k" here represents kilos. So, the number 181,800 is indicated.

Q: How many MJ kg is 6530 kcal?

A: 1 kcal is joules, and 1 kcal is 1000 kcal. So, 6530 kcal is 6530 1000 = 6530000 kcal.

To convert 6,530,000 calories to a megajoule (mj), you need to search for 1,000 1,000, i.e.: 6,530,000 calories 1,000 1,000) = megajoules. Yes, 6530 kcal is commensurate with megajoules.

In addition, 1 kilocalorie is 1 kilojoule (kj), which can also imply 6530 kilojoules (kj) kilograms.

Q: What is the score of 2-55 72?

a: 2-55 72 can first convert 2 into a fraction, i.e. 2 = 144 72, and then subtract and obtain: 2 - 55 72 = 144 72 - 55 72 = 144 - 55) 72 = 89 72.

Therefore, the score of 2-55 72 is 89 72.

You're two to the fifth power! Then cut it from the middle.

The fifth power of two was originally 32. Cut it from the middle of the state god again, and the imitation mu will become 64 paragraphs. Prepared Forest.

2 to the nth power plus 1 paragraph.

Seek to be like a stalk. Because the fold is cut in half once from the middle, there is a hole 21 + 1 = 3 (segments);

Fold in half 2 times and cut from the middle, there are 22 + 1 = 5 (segments);

Fold in half 3 times and cut from the middle, there are 23 + 1 = 9 (segments);

The slag hand is cut from the middle 4 times, and there are 24 + 1 = 17 (segments).