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 solution by Charlie)

Actually I was over-cautious in adding up to 350 in carries. A 9 in the 5th significant digit, with subsequent 9's can at most be equivalent to 1 in the fourth significant digit, and when multiplied by the max of 35, would be 35 at most, so 350 is overkill.

Posted by Charlie on 2022-08-12 19:43:16