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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: ( Back to comment list | You must be logged in to post comments.)
Question re: An attempt as (3), but it looks wrong according to simulation | Comment 7 of 12 |
(In reply to An attempt as (3), but it looks wrong according to simulation by Charlie)

I really would like someone to see if I made a logic mistake or some algebraic error, as the simulation result seems too out of line with the analytic calculation for part (3).
  Posted by Charlie on 2011-03-30 09:57:59

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