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 re(2): The answer to this puzzle, the universe, and everything by broll)

Yes, but the puzzle asks about all real numbers, including 0.166666...

Posted by Steve Herman on 2022-08-14 07:37:14