Can you please share how you got the 2^40 number? I've been trying to think of how to figure out the odds of these.
Odds of 4 hex 8's in a row given a 4 digit string is (1/16)^4.
Odds of 4 hex 8's in a row given a 5 digit string is
number of ways to arrange 8s in the first 4 digits (1) times 16 possible 5th digits plus number of ways to arrange 8s in the last 4 digits (1) times 16 possible 1st digits, all divided by the number of possible arrangements (16^5)
Odds of 4 hex 8's in a row given a 4 digit string is (1/16)^4.
Odds of 4 hex 8's in a row given a 5 digit string is number of ways to arrange 8s in the first 4 digits (1) times 16 possible 5th digits plus number of ways to arrange 8s in the last 4 digits (1) times 16 possible 1st digits, all divided by the number of possible arrangements (16^5)
So 8888X or X8888 is (2 * 16) / (16^5)?
And then 8888XX or X8888X or XX8888 is...
(16^2 + 16^2 + 16^2) / (16^6) ???