Prove: If x is a positive real number, then somewhere in the infinite sequence {x, 2x, 3x, ...} there is a number containing the digit 7.
If x is a positive real number, then somewhere in the finite sequence {x, 2x, 3x, ..., nx} there is a number containing the digit 7. Find the minimum value of n.
Note: Some numbers can be written in two ways (1.8=1.7999999...) only consider the form without all the 9's.
Source: Slightly adapted from a post by Victor Wang on Facebook.
(In reply to
Part I proof by Steve Herman)
I'm not sure your proof is sufficient. Just because the set of positive integers is infinite, that does not guarantee that every space on the slide rule is hit. It's still possible some interval is missed every time.
This reminds me of people saying every possible finite digit sequence occurs somewhere in pi. This seems plausible but has not been proved true. https://en.wikipedia.org/wiki/Normal_number
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Posted by Jer
on 2022-08-12 08:59:43 |
re: Part I proof
