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Powerful Digit (Posted on 2011-03-29) Difficulty: 3 of 5
For a randomly chosen real number x on the interval (0,10) find the exact probability of each:

(1) That x and 2x have the same first digit

(2) That x and x2 have the same first digit

(3) That x2 and 2x have the same first digit.

(4) That x, x2 and 2x all have the same first digit.

First digit refers to the first non-zero digit of the number written in decimal form.

No Solution Yet Submitted by Jer    
Rating: 4.0000 (1 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(3): answersCharlie2011-03-30 14:20:40
re: An attempt as (3), but it looks wrong according to simulationJer2011-03-30 14:10:39
re(2): answersDej Mar2011-03-30 13:10:44
re(2): part (1) not so hard after all (spoiler)Charlie2011-03-30 10:57:13
re: part (1) not so hard after all (spoiler)Jer2011-03-30 10:01:43
Questionre: An attempt as (3), but it looks wrong according to simulationCharlie2011-03-30 09:57:59
Some Thoughtsre: answersCharlie2011-03-30 09:56:27
Possible solution to part 4.broll2011-03-30 07:51:56
answersDej Mar2011-03-30 04:17:59
Some ThoughtsAn attempt as (3), but it looks wrong according to simulationCharlie2011-03-29 22:27:42
Some Thoughtspart (1) not so hard after all (spoiler)Charlie2011-03-29 17:31:49
Some Thoughtspart (2) -- the easy one (spoiler for this part)Charlie2011-03-29 17:03:54
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