Solve This Math Problem WITHOUT a Calculator! | Fast & Easy Tutorial

[andrewg.carvill]

My father used to love the following puzzle: You take a large sheet of thin paper, 0.1 millimeter thick, tear and double it over, tear the two and double them over, tear the four and double them over, etc, etc. If you tear and double 50 times in total, how tall will the stack of small paper fragments be at the end? With logarithms or a calculator it's quite easy to work out the answer, but you have to guess before doing any calculations. Hint: if the original page had the same area as the continent of Africa, the paper fragments in the tall stack of paper at the end would each be about 5 cm by 5

[pedroloures]

That's interesting, in order for you to calculate the value you used the number 20, which is simple to work with! Very good!

[myobboy]

I am an engineer, it took me 5 seconds to say that the answer is slightly less that 3.2 million. (2^5 x 10^5). You show us how much less than 3.2 million and that is 1.25% in this special case of the number 20 and an arithmetic span of 4. Well-done. Plot the function of how much less than x^5 for all x and you will find that as x tends to much larger than the arithmetic span, the error in the x^5 function becomes assymototic to zero and hyper-stable as x becomes much larger than the arithmetic span. At 5 itself, the error in x^5 (span 4) is about 20% too high. At x = 3 the error is a horrendous 50%, so, only use my approximation method for In the case of your example, x = 5 times the arithmetic span of 4. At x = 3, the x to arithmetic span ratio is a highly dangerous 0.75.

[njordholm]

Dear Sir,

I like your videos and watch them on a regular base... often at night, when nothing is on TV 😅, so I also have YouTube in dark mode.
The one thing, which I like to request, is to exchange colours.

I always get blinded by the bright white background, even if I set backlight to low on my device. Best for me would be white text on black or dark grey background. But black text on a lighter grey background would be of help as well.

Perhaps you like to consider this in future videos.
Anyways, thanks a lot for discussing math topics and offering solutions.

Regards

[silviatotaro]

I often control my expences in the way you showed in the video. People look at me with suspition.... Now, I can show that I am not alone! Greetings from Italy!

[akshaybisen]

I always give a try before continuing the video. I was right This time as i know this method of multiplying consecutive numbers when i was in 10th standard. Thanks a lot for bring back the memories.

[joyona]

Thank you. I am learning a lot from viewing your videos.

[focusconsistency]

I'm so grateful to this channel. Thankyou sir! ⚡

[walkerable]

Great tutorial making use of our old friend Mr Algebra to fascinating use

[holyshit]

18x22 - difference of two squares
19x21 - difference of two squares
396x399 - distributive property
multiplication by 20 is easy
In mental calculations it is easy to get lost
I calculated it but it took me more time than i expected

[jayantadas]

Your channel is extraordinary. Please upload problems on number theory too.

[wackojacko]

Good morning sir...I have a four colored pen...do you use Apple IPAD? I love the organization.
Btw, , , , when you look at an equation like this...what is the logic you use to lead you to X = 20? What happens if I use X = 18.? ...a big mess I assume.

[brucehutchinson]

When I was in school this is how we did all math. In College with the help of a slide rule.

[andrewg.carvill]

If you multiply 98 X 99 X 100 X 101 X 102 then X can be 100 and the product is 9, 995, 000, 400. The 4 and the 5 in the formula 'stay visible' in the product.

[KusumaWijaya]

Nice approach, cause normal one will use perkalian bersusun

[math]

interesting method, very well explained, thanks for sharing

[omarafify]

Thank you for this helpful and simple explanation ❤️

[prohind]

It's like catching the nose from behind one's head.

[janes]

That was very long-winded. It took me less than 1 minute using a piece of paper, a pencil and long multiplication.

[petekutheis]

plain old long multiplication works for me, , lol.. yes product of the 60s and 70s.