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7 somewhere (Posted on 2022-08-12) Difficulty: 4 of 5
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.

No Solution Yet Submitted by Jer    
Rating: 5.0000 (2 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(4): solutionCharlie2022-08-15 16:57:51
re(3): solutionSteve Herman2022-08-15 08:25:26
re(2): solutionCharlie2022-08-14 20:15:43
re(4): The answer to this puzzle, the universe, and everythingbroll2022-08-14 09:22:26
re(3): The answer to this puzzle, the universe, and everythingSteve Herman2022-08-14 07:37:14
re(2): The answer to this puzzle, the universe, and everythingbroll2022-08-14 03:02:25
re: solutionSteve Herman2022-08-13 20:42:04
re: The answer to this puzzle, the universe, and everythingSteve Herman2022-08-13 20:37:02
SolutionThe answer to this puzzle, the universe, and everythingMath Man2022-08-13 10:26:42
re: solutionCharlie2022-08-12 19:43:16
SolutionsolutionCharlie2022-08-12 15:03:15
Proof for 1st Part (not smallest)H M2022-08-12 11:06:44
Possible Solutionbroll2022-08-12 09:31:47
re(2): Part I proofSteve Herman2022-08-12 09:19:04
re: Part I proofJer2022-08-12 08:59:43
Some ThoughtsPart I proofSteve Herman2022-08-12 08:04:19
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