How many unique answers are there to all the natural whole numbers 1 - 99 multiplied by all the natural whole numbers 1-99? For instance all the single digits 1-9 multiplied by all the single digits 1-9 yields 32 unique answers between 1& 81. Do the graphs of these 2 problems show any fractal properties. What about 1-999 multiplied by 1-999
double digit sums 1-99 * 1-99
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combinatorics
algebra-precalculus
arithmetic
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1Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. – 2012-11-21
1 Answers
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I calculate that there are, in fact, 36 unique products $ij$, with $1 \le i,j \le 9$.
For $1 \le i,j \le 99$, I find 2869 unique products.
For $1 \le i,j \le 999$, I find 247814 unique products.
I'll need to know more about what you mean by "graphs of these 2 problems" to say anything about fractals here.
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0@fineshigher Great, but I cannot seem to find it anywhere. Could you put it in a comment? – 2012-11-21