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:
Cross out each row that has an even number in the left column, and add the numbers that remain in the second column:
That gives the right answer (97 × 23 = 2231). Why does it work?