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When I was in grade school, I just couldn't face the mind-numbing rote memorization of the 12x12 multiplication table. It was, to my mind, an insanely ridiculous exercise in redundant, repetitive effort. "Busy work." It provoked such enormous and deep-seated resistance in me that there was no question I'd NEVER memorize it. So ...
I examined it and found that I could cut the memorization task down to almost nothing. I noticed, first of all, that the answer to 8x12 was the same as the answer to 12x8 ... and, indeed, it made no difference what pair of numbers were multiplied -- the answer was the same no matter which came first. Voila! I cut the task almost in half. Next, I noticed that 8 times anything was the same as double 4 times the same number. The same for 6 times anything being double 3 times anything. In fact, when ANY even number was multiplied by anything, I could merely double the answer for half of that number.
By the time I was done, I'd pared the task down to less than 1/10th the size. Instead of memorizing 144 separate answers for every pair of numbers between 1 and 12, I needed learn less than 12. It was only years later that I learned about prime numbers, the associative law, and the commutative law. After all, I'd DISCOVERED them all by myself. Because I was lazy.
Even today, nearly 60 years later, I cannot 'remember' the answer to 8 x 7 ... and must multiply 7 x 2 x 2 x 2 (getting 14, 28, and 56) to get the answer of 56. I'm STILL lazy.
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