What is the first 10-digit number in the decimal expansion of pi that contains each digit exactly once?

(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:

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

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

**2**^{nd }: 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) 5^{th} row: even s.b. **event**

** 2)** 8^{th} 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**