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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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re: computer solution | Comment 2 of 3 |
(In reply to computer solution by Charlie)

I was surprised by how soon the condition occurs. 
For 10 random digits the probability of each digit once is 10!/10^10 = .00036288 ≈ 1/2756
For an even with this probability to happen in 60 tries or less using a geometric distribution is just over 2% chance.

Finding 35 occurrences in 100,000 digits is perhaps less than expected
.00036288*100000=36.288 which is pretty close to 35.

Also surprising: only two pairs with immediate overlap and they are  the first two.

  Posted by Jer on 2015-08-21 12:11:49

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