Granth Thakkar's world record for 20 digit multiplication

Mental Calculation, Mathematics, and Puzzles
1

First of all, it is a fantastic feat.
I think you mean this video: https://m.youtube.com/watch?v=bU0kRBG9hm4

What he does is the criss cross method. From right to left.
A good explanation of this system is found here: http://www.sapnaedu.in/multiply-any-4-digit-numbers/

He uses his fingers to keep track of where he is.
You see the same thing happening in the crosses in the previous link:
http://www.sapnaedu.in/wp-content/uploads/criss-cross_41-567x1024.png

The dots outside the cross in each step do not have any function and that is why Granth is hiding them with his fingers.

If you want to be able to calculate this way from left to right, without using fingers, looking at a screen, or writing sub totals down, start small.

Start by doing a lot of 2x2’s daily.

Since you said that you wanted to memorize the squares from 16 and higher, just do this. In your mind square 16 by using the criss cross method.

So try to see:
16
16
__*

Then do 10*10, 6*1+6*1, 6*6 = 100 + 120 + 36 = 256

Then, once you feel proficient with the 2x2’s, move to 3x3’s.
If you can do a 3x3 mentally you can do more than most humans.

Duplex method for squaring numbers very quickly
2

Thank you for the post! I’m going to try to work up to 3x3’s with the criss cross method. Quick question: Do you know what he uses for square roots? Is it the Doerfler method?

3

When you do, check out this post: https://artofmemory.com/forums/avoiding-the-carry-5494.html
The basic idea is that sometimes it is better to see 69 as 70 - 1 instead of 60 + 9 (which is how you would pronounce it).

Some criss cross calculation become a lot easier to do this way.

4

I don’t know. Maybe Nodas, who does go to the mental calculation championships, knows.

In general, to be very fast at taking roots, you need an algorithm when the remainder does not grow quickly.

The algorithm that used to be taught in high school:

is an example of an algorithm where the remainder grows, and grows, and grows.
For that reason it is unsuitable for calculating with 8 significant digits as you need to be able to do in championships.

When step can to be calculated quickly and the remainder stays small, then you can be quick.

Granth can do 10 roots in just over 1 minute: Mental Calculation Records: Extracting Roots
and this is pretty amazing.

5

Thanks again, Kinma. You’ve taken a lot of time to explain things to me and I really appreciate it. :slight_smile:

6

Hi all. Kinma suggested that I reply to this topic.

Firstly, I am the one who recorded that video of Granth doing the 20x20 correctly, in Germany. Later, I put those videos my “MentalCalculation1” channel in Youtube, just for the Dresden MCWC 2014 World Cup. I don’t think I’ll put many videos there soon, since I’m doing some kind of rebranding. Anyway, I recorded that particular video of Granth, on 12 Oct. 2014, in the “Holidays Inn” Hotel in Dresden, Germany. I was recording Granth during his official trial and I witnessed him solving correctly the whole 20x20 multiplication thing in less than 3 minutes. Yusnier Viera, Silke Betten, Jan Van Koningsveld, Melik Duyar and Scott Flansburg, were also present in the room in this official trial. (along with Rhea Shah who broke the 10-digit Roots record). Scott Flansburg was so ecstatic about Granth, that he told us “If I am the Human Calculator, then Granth is the Machine Calculator himself” !!. But unfortunately, neither Granth nor Rhea competed in 2016. That’s was a shame because I was really interested to see how the Top Indians would fare against the Top Japanese and Mrs. Lee from S.Korea. The Indians in 2016, besides Calendars, did not really win many golds, because of these 2 extremely important absences of Granth and Rhea.

About the square root method, since I have been a Memoriad medalist on roots almost 5 years ago in 2012, I’d just like to mention that I quickly learned Rob Fountain’s, Jan V.K.'s, and Willem Bouman’s method, just after MCWC-2010 and in 1 year I saw and I was really efficient in it. I won’t mention the algorithm, here, because it’s already posted numerous times in the YAHOO’s MC group. Just search through the posts there from 2010 to 2012. And everyone does his own shortcuts, which are kind of a personal effort, like learning the 1000 squares or something. Talent is not enough. It needs willingness to train.

About Granth, Rhea and the Indians, they use the “Duplex Method” which is far more efficient than ours, but to each his own. Personally, I stopped training so much in square roots, because I had to devote my time to become better at Calendar calculation where I had many more chances to reach the Top. In roots, in competitions I just try to keep up with the level I am now. It’s hard to improve much more, at my level, unless I switch to the Duplex method, and I am not really into mood for that right now, because it’s a whole different thing and needs to re-tame another mental beast. And the World Records in both roots and calendars are now so high, where there is very little human room for substantial improvement.

Regards,
Nodas, Greece

1 Like
7

Thank you so much for your post, Nodas. It was very informative.

This seems to hold true for many things. I was recently talking to somebody about the piano. I was explaining how talent alone isn’t enough. You need a lot of practice. The same goes for engineering. Tesla, for instance, was naturally brilliant, but he still had to study for obscene lengths of time to achieve what he did (If I recall correctly, he reportedly studied up to 15 hours/day.).

8
About Granth, Rhea and the Indians, they use the "Duplex Method" which is far more efficient than ours

Hi! Could tou please tell me the difference between the Duplex Method and the general Square root algorithm used by yourself and Jan van Koningsveld? I learned in the MC Group the general algorithm, and have been practising for some time. My personal record is 5 and a half minutes to solve 10 tasks of 6 numbers each. But I would definetely change the method, if that meant increasing speed.

Sorry if my english isn’t good…I’m from Brazil!

Daniel Castro

9

In the “general method” you start from the nearest perfect 3-digit square, so you get the first 3 integer digits instantly. After that you divide with the first 2 digits, subtracting the cross-products and so on.

But in the Duplex method you just start from the first 2 digits and then divide by 1-digit only. At a first glance , this seems easier, but the subtracted cross-products are longer and more complicated and it’s easier to miss the 8th digit and lose everything.

There are some shortcuts in the Duplex though, and I think the best in the world (Granth, Shashank and Rhea and many of the “Genius kid” Mumbai team), have already memorized many tables with the first 3-4 digits, so sometimes they can solve the whole 8 digits in less than 6 seconds, in each task. I will compete against Granth soon in the Mental Calculation World Cup 2018 this year, but these things are kinda secret for each top-competitor, so it’s hard to ask them about “what root tables have they exactly memorized”.

About the Duplex, you can see roughly how it works, from my photograph from MCWC 2010. I was not so efficient back then, so my friend Arturo Mendoza from Peru was explaining the Duplex in that paper to me, because I wanted to start solving all 8-digits. But then during 2012 I decided to skip that Duplex so I started practising with the other “general algorithm” (Jan/ Willem/ Robert’s), because in practice I was more accurate with that. In Memoriad '12, using that general method and I was able to solve all 10 correct, and thankfully for me, all the best root-solvers in the world, Jan, Hakan, Naofumi, Rhea, and Granth, were all out of shape that day and they made mistakes, so I got my 2nd place.

But the MCWC competition now has tougher rules for the square roots. If you lose the 8th digit then you lose everything, for example if you solve 6 digits like you said, then you get 0 points according to the official MCWC rules and not 21 points like in the Memoriad program, for 6 digits respectively.

10

Thanks for your explanation! I think i wasn’t clear. I solve 10 Square roots of 6-digit numbers for all 8 digits.

I was using a 2 digit estimate and 2-digit divisor, and someone told me that using 1 digit was faster because of the division. Then, I began to use a 1 digit estimate (I didn’t know it was possible to use 2 digit estimate and 1 digit divisor. How do you do the carries?

11

I suggest you read this Yahoo MC group post from Willem Bouman in 2008. It’s about this “general method” which I described, and it has already been explained many times in the MC group. In that post, Willem wrote that Jan van Koningsveld, Gert Mittring and Robert Fountain taught this method to him. This method is also included in Jan & Robert’s book called The Mental Calculator’s Handbook.

12

Thanks!

13

Hi.

“There are some shortcuts in the Duplex though”

What shortcuts do you know for the duplex method?

One can divide everything by 2 as in the general method. Do you know whether the Indians do it too?

Also, sometimes the divisions of the cross products can be simplified with some creativity, as in 62/7 = 9 r -1 = 8 r 6 instead of calculating 62-56 or when a negative remainder is expected, as in 64/7, not to calculate 64-56 but 64-63+7. Of course, the standard method is also a very easy calculation and I don’t know why but somehow it makes the process more fluent, especially for larger divisors, when I have to switch to a two-digit divisor.

Where is the border when duplex method calculators switch to a two-digit divisor? For example, calculating a root with a 1 or even a 2 as it’s first digit seems almost impossible to me with a one-digit divisor.

Are there other shortcuts, for example for reducing the chance of the negative remainder issue, something for rounding the last digit or some memorization that makes things easier? I have found nothing that really explains the Indians’ method in detail, but what do you know about possible simplifications?

2 Likes
14

Hello.

Firstly, this is a wrong thread to discuss roots, since it’s about a multiplication record.

Secondly, even if it was a root thread, all the things you asked probably require a specific book or a very specialized article.

Thirdly, like I wrote, I never used the duplex method myself. I just had several discussions with people who used it it.

Fourthly, the shortcuts I mentioned include a huge memorization of tables but that’s usually only for people who compete at the top level and can solve a 6 digit to root to 8 significant digits in 10 seconds. The world record is less than 5 seconds per such root, and I am sure this includes more memorization of tables (such as all the initial 3 integer digits).

If you are still extremely interested in improving roots, then I recommend to google and try to locate and ask in social media, all the people who have solved all 10 6-digit roots in less than 3 minutes. Most of them are Indians and use the Duplex.

My competition best is around 14 minutes
(like in my Square Roots Silver Medal in Memoriad 2012) and my personal training best is around 11 minutes for all 10 roots. But that was around 10 years ago, and the solving methods globally have improved a lot since then.

And like I wrote, as someone who has not used the Duplex method, I cannot give further insights about how then manage to solve all roots in 1-2 minutes, or even 5 minutes with the Duplex .

Since that skill is beyond my capabilities and beyond the efficiency of my algorithms.

1 Like
15

Just a tip, @Kinma , if you prefix the stars you use for writing multiplication with a backslash, you will ensure that the numbers don’t turn into cursive text, like so: *53*
The symbol alone, typed using two consecutive backslashes: \
I think this would help the readability of your posts, and since you seem to know a lot about mental maths and your posts are abundant, I think you should do this to improve your (future) posts.
You can decide to edit or not to edit your past posts yourself, that’s on you.
Thank you for understanding either way.

1 Like
16

Thanks for the tip, Marty!

I usually proofread my comments, twice. So this might have slipped my attention. I changed my post.