# How many people would it take to mentally multiply 2 three digit numbers?

Okay, this is kind of a silly exercise, but I think it would be fun to try out to see if it works. It might make a good project for an elementary school class. I say that 5 ordinary (or perhaps mildly deranged) people could collectively mentally multiply 2 three digit numbers.

First of all you have to recall what it was like to multiply numbers on paper. You formed 3 rows by multiplying the top number by each digit of the bottom number and then added them together.

Here is how it would work. One person acts as the multiplier. He would announce in turn each digit of the first row, which another person would be responsible for memorizing. The other two rows would be assigned to two other people. To add the three rows, the multiplier points to each of three row people who will sequentially tell the last digit of their row. The mulitplier adds these numbers, keeps track of the carry and announces the last digit of the product, which would be kept track of by the fifth person. Then the multiplier points in turn to each of the row people, who tell the second to last digit of their number, which the multiplier adds together, combines with the carry and announces to the person keeping track of the product. And so on.

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I bet i could do it in my head. Unless there’s some catch to it….or maybe I’m missing something?

Yeah, but could they calculate the cube root of pi?

wundayatta (58591)

Your exercise would probably work, but I know I could definitely multiply that in my head myself. Mental exercise is good for you, it really bugs me when I see people open their cell phone to figure out how much tip they owe the waitress.

jlm11f (12363)

This wouldn’t be that difficult to do on your own.

Ivan (13439)

The classic blunder:
1. Man exercises mind and invents calculator
2. Man exercises calculator and atrophies his mind

I give credit to those who say they can multiply two three-digit numbers in their head. The answer could have up to 6 digits. It takes a certain amount of effort just to memorize 6 digits. I think I could mulitiply any two two-digit numbers, but I do not know if I could go beyond that.

You might be interested in this” Mathemagic

Les (9612)

I think I can multiply 3-digit numbers in my head, though it would of course be a lot easier to multiply something like 348×150 than it would be for 793×897. But I still think I could do it. I’m pretty good at simple arithmetics (and geometry) but crap at more complicated stuff.

Jack79 (10984)

Don’t get me wrong, it would probably take me quite a while. But I bet I could do it.

Ivan (13439)

Yep, what @Ivan said.

jlm11f (12363)

I could definitely multiply two 3 digit numbers in my head…I couldn’t do it quickly, but I could do it. But aside from that, the logic in the hypothetical exercise seems to be sound.

dalepetrie (18007)

whatthefluther (13807)

OK, I’m going to use the example above, I’m starting at 5:14 pm, the exapmle being the one @Jack79 posted of 793×897. First thing I’d do is look at that second number and see that it’s only 3 away from 900. So I’d say to myself, what is 793 times 3. and I could do that pretty easily…2379. Then I’d say, what is 793 times 900 and subtract 2379 from it. And in fact, I’d probably say, the easiest thing to do is to say that 900 is exactly 100 less than 1000. And it’s easy to multiply numbers by 100 or 1000, just add 2 or 3 zeros. So I’d say, OK, what’s 793 times 1000? Well, that would be 793000. Then I would say, what is 793 times 100, well that would be 79300. So to get at what 900 times 793 is, I’d simply have to subtract 79300 from 793000, which would get me to 713700. Now to get to 897 times 793, I’d just have to subtract 3 times 793, or 2379 from that number. That would give me 711321. OK, it’s 5:17, double check my calculator to see if I’m right….bingo.

I’d submit anyone with the wherewithall could do it, it’s just a trick of breaking the numbers down into 10s, 100s and 1000s places, take it one step at a time and bingo, 3 minutes to multiply 2 very large 3 digit numbers and come up with an accurate 6 digit result.

dalepetrie (18007)

100×100 = 10,000.
It only took me a half sec to do that in my head.

AstroChuck (37357)

yeah after I gave my example I realised 897 is only 3 away from 900 which is only 100 away from 1000. That’s the exact way I’d do it too. But then again the idea was not to give the hardest possible combination. If you’re lucky enough, the two numbers you have to calculate could be 100 and 200, or at least 300×999.

breaking numbers:
x9=x3×3
x8=x2×2x2
x7=pretty tough one, I usually do it as x2×2 + x3. If I don’t have to be precise (eg currency rates) I do it as 2/3×10
x6=x2×3
x5=half of x10
x4=x2×2
x3 simple
x2 simple

any number can be broked down into a combination of the above simple sums. The only problem is remembering the individual numbers so you can add them up at the end.

Jack79 (10984)

@jack79 – and if you can remember 3 peoples’ phone #‘s, you should be able to do that, right?

dalepetrie (18007)

@Les , Thanks for the link. There was one trick that he did that was actually fairly simple. He asked people to mulitply a particular number by any other number and tell all the digits except for one. The number chosen for mulitplying was divisible by 9, so the answer was divisible by 9, and the missing digit could be found by casting out 9’s. The only problem would be if the missing digit was a 0 or 9, because it would not be possible to distinguish between the two of them.

@dalepetrie ok so I remember my own number, my parents’ home number (the same since 1977) and my best friend’s number so yeah. I don’t think I could name a fourth. Oh yeah, my old number when I lived with my aunt. Haven’t memorised a single one since the invention of the mobile phone. I don’t even know my sister’s.

Jack79 (10984)

@Jack79 – true, I forgot that since cell phones people don’t actually know their own friggin’ numbers anymore. It always cracks me up when I hear someone stumble trying to come up with their own phone number…then it makes me feel old…then I feel sad. Usually then I have something to eat.

dalepetrie (18007)

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