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)
Charlie, your last approach, involving the last digits of a real numbe,r is a little suspect, as some real numbers have an infinite number of digits. Is it possible that your method only works for integers, or for rationals that are not repeating decimals?
re: solution
