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Two by Two

Here’s a curious way to multiply two numbers. Suppose we want to multiply 97 by 23. Write each at the head of a column. Now halve the first number successively, discarding remainders, until you reach 1, and double the second number correspondingly in its own column:

two by two - first image

Cross out each row that has an even number in the left column, and add the numbers that remain in the second column:

two by two - second image

That gives the right answer (97 × 23 = 2231). Why does it work?

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