In a 1975 essay, Martin Gardner presented a trick for multiplying two large numbers, when one of the numbers was given by the operator. The explanation of trick involved factoring a number that was one more than a power of ten, thereby obtaining one of the factors being multiplied. In this paper, we explain how to choose one of the factors without needing the factorization step.
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Brubaker et al. (2024) studied this question.
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