A random factoid from Cheaper by the Dozen:

Also of exceptional general interest was a series of tricks whereby Dad could multiply large numbers in his head, without using pencil and paper. The explanation of how the tricks are worked is too complicated to explain in detail here, and two fairly elementary examples should suffice.

1. To multiply forty-six times forty-six, you figure how much greater forty-six is than twenty-five. The answer is twenty-one. Then you figure how much less forty-six is than fifty. The answer is four. You can square the four and get sixteen. You put the twenty-one and the sixteen together, and the answer is twenty-one sixteen, or 2,116.

2. To multiply forty-four times forty-four, you figure how much greater forty-four is than twenty-five. The answer is nineteen. Then you figure how much less forty-four is than fifty. The answer is six. You square the six and get thirty-six. You put the nineteen and the thirty-six together, and the answer is nineteen thirty-six, or 1,936.

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