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.
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.
n is no larger than 35, since 2*35=70.
For all other numbers, it suffices to consider the 12 times table, and the numbers 20,22,33,55,66,166 to prove that no larger candidate can exist.
Edited on August 12, 2022, 9:58 am
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Posted by broll
on 2022-08-12 09:31:47 |
Possible Solution
