The Russian Peasant Algorithm

Ken writes:

A friend sent me a link to an intriguing youtube video demonstrating a visual method for multiplication used by the ancient Mayans.

But if you google ‘Mayan multiplication’, you also get a discussion of something called the “Russian peasant algorithm” a method of multiplying two numbers used by the ancient Egyptians and Romans as well as the Mayans.

You take the two numbers to be multiplied and write them beside each other

789, 6573

Then you double one and half the other, discarding any remainders as you halve them.

394 , 13146

You also have to cross out a line when the number on the halving side is even.

197, 26292

98, 52584

49, 105168

24, 210336

12, 420672

6, 841344

3, 1682688

1, 3365376

Finally, when the halving side has got down to one, you add the numbers on the doubling side that haven’t been crossed out, including the first number. The sum of these numbers is the product of the original two numbers.

5186097

Now doesn’t that just seem utterly absurd? And yet it works!

The Roman method is explained in more detail here. The Russian peasant algorithm is explained in detail here.

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4 thoughts on “The Russian Peasant Algorithm

    1. kenanddot

      I also found the explanation of why it works completely baffling, which is why I didn’t attempt to explain it in the post. The links at the bottom do go some way to explaining it but I fear I stopped well short of full understanding.

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