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(3): solution by Steve Herman)

I haven't found anything higher than 42, but I can't be sure I haven't thought of all the possible sources of error.

Posted by Charlie on 2022-08-15 16:57:51