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One of my favorite techniques is that which allows us to multiply any number long with 11.
To get your attention I will say that I can multiply in my head the following numbers:
748346274 x 11 = 8231809014
The technique is quite simple:
- the last digit of our product will be the last digit of number which is not 11 (e.g. 748346274) : 4
- the next digit of our product is calculate by adding the n digit to the n-1 digit: 4 + 7 = 11; we write down 1 and save 1 into memory
- the next digit of our product is calculated by adding the n-1 digit to the n-2 digit: 7 + 2 = 9; recall the 1 saved previously so we get 10; the next digit of our product becomes 0 and save 1 into memory
- the next digit of our product is calculated by adding the n-2 digit to the n-3 digit: 2 + 6 = 8; recall the 1 saved previously so we get 9; the next digit of our product becomes 9
- we continue the process until to the first digit (on the left) of our number; that way we obtain the final product as 8231809014
Very simple!