All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 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)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: part (1) not so hard after all (spoiler) | Comment 8 of 12 |
(In reply to part (1) not so hard after all (spoiler) by Charlie)

Since the first digit cannot be zero,  it is actually 1/9 of the numbers on the interval (0,1) that begin with the digit 1, not 1/10.

Your solution is too small by 1/900.

 Posted by Jer on 2011-03-30 10:01:43

 Search: Search body:
Forums (0)