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Trachtenberg defined this algorithm with a kind of pairwise multiplication where two digits are multiplied by one digit, essentially only keeping the middle digit of the result. By performing the above algorithm with this pairwise multiplication, even fewer temporary results need to be held. Example:
[1] [2] [3] It is a divide-and-conquer algorithm that reduces the multiplication of two n-digit numbers to three multiplications of n/2-digit numbers and, by repeating this reduction, to at most single-digit multiplications.
More formally, multiplying two n-digit numbers using long multiplication requires Θ(n 2) single-digit operations (additions and multiplications). When implemented in software, long multiplication algorithms must deal with overflow during additions, which can be expensive.
2: 12 "Nine Nits is all there's Room For" Addition and subtraction less than 10,000 3: 13 "Breaking up is Easy to Do" Multiplication 4: 14 "You Ain't Nothing but a Houndred" Multiplication of 3-digit numbers by single digits 5: 15 "Dividing we Stand" Dividing 3-digit numbers by 2-digit numbers 6: 16 "Double Digit Dating" Multiplying double ...
Mixmath is designed for 2 to 4 players in games lasting roughly 60 minutes. ... 99 that can be represented as a multiplication of two numbers between 1 and 10 (for ...
The same is done for each digit of the multiplicand and the result in each case is shifted one position to the left. As a final step, all the individual products are added to arrive at the total product of the two multi-digit numbers. [69] Other techniques used for multiplication are the grid method and the lattice method. [70]
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