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 Powerful Digit (Posted on 2011-03-29)
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)

 Subject Author Date re(3): answers Charlie 2011-03-30 14:20:40 re: An attempt as (3), but it looks wrong according to simulation Jer 2011-03-30 14:10:39 re(2): answers Dej Mar 2011-03-30 13:10:44 re(2): part (1) not so hard after all (spoiler) Charlie 2011-03-30 10:57:13 re: part (1) not so hard after all (spoiler) Jer 2011-03-30 10:01:43 re: An attempt as (3), but it looks wrong according to simulation Charlie 2011-03-30 09:57:59 re: answers Charlie 2011-03-30 09:56:27 Possible solution to part 4. broll 2011-03-30 07:51:56 answers Dej Mar 2011-03-30 04:17:59 An attempt as (3), but it looks wrong according to simulation Charlie 2011-03-29 22:27:42 part (1) not so hard after all (spoiler) Charlie 2011-03-29 17:31:49 part (2) -- the easy one (spoiler for this part) Charlie 2011-03-29 17:03:54

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