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Numbers in pi (Posted on 2015-08-21) Difficulty: 2 of 5
What is the first 10-digit number in the decimal expansion of pi that contains each digit exactly once?

No Solution Yet Submitted by Math Man    
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Hints/Tips re(2): computer solution surprised?? Comment 3 of 3 |
(In reply to re: computer solution by Jer)

I am truly surprised that you are surprised!

Mathematician should not be shocked that an event with an   a priori (=calculated before the event) low probability pops up too soon.  BTW 2%  is not low,  maybe 10^(-20) is.

It is a common fallacy to confuse   a priori  and  a posteriori  results, especially  considering random sequences.

Consider two examples, both based on the pi expansion chain, presented by Charlie:

1st:  What is the probability that the first zero appears after 32 non-zero digits?

Answers:   nil   a priori and   100%   a posteriori  results.

2nd :    let the chain  1415926535…ETC   (100 digits) be denoted by SEQ100.

  What is the probability that  SEQ100 (i.e.14159265…ETC ) will be the sequence appearing  after the decimal point in the pi expansion chain, presented by Charlie:?

Answers:   nil   a priori  and  100%   a posteriori  results.

 

Two minor remarks:   in your post 

           1)   5th row: even s.b. event

           2) 8th row:  “is perhaps less than expected “  s.b. “is quite close to the expected value”.

 

It would be nice to correct those two expressions for the benefit of future readers.

Please comment.

Edited on August 22, 2015, 2:28 am
  Posted by Ady TZIDON on 2015-08-22 02:27:39

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