What is the first 10-digit number in the decimal expansion of pi that contains each digit exactly once?
(In reply to computer solution
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