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West Side Story (Posted on 2004-02-15) Difficulty: 4 of 5
Does 9 appear as the leftmost digit in the decimal representation of any power of 2?

Does 7 appear as the leftmost digit in the decimal representation of any power of 37?

Is it possible to find a power of any counting number that has a given digit as its leftmost digit?

Also, is it possible to find a power of any counting number that begins with a given series of digits (e.g., is there a power of 24 that begins with 937)?

Prove that this is possible, or give a counter-example.

Bonus: What percentage of the powers of 2 have 1 as their leftmost digit?

Note: In finding the powers of "any counting number," exclude powers of ten, whose leftmost digit is always 1.

No Solution Yet Submitted by DJ    
Rating: 3.2500 (8 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Puzzle Answer K Sengupta2023-07-30 02:46:31
SolutionSlide Rule logic (spoiler)Steve Herman2012-03-04 11:22:42
re: Initial numbersFederico Kereki2004-02-16 09:53:45
re: Initial numbersSilverKnight2004-02-16 09:14:05
SolutionInitial numberse.g.2004-02-16 08:07:16
re(2): SolutionCharlie2004-02-15 15:18:08
Questionre: SolutionPenny2004-02-15 13:01:34
SolutionSolutionCharlie2004-02-15 10:34:43
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