You are mistaken: my guess is that you are taking the square root because of the birthday paradox, but that is incorrect, and the birthday paradox does not apply here anyway.
The probability of generating a hash with the right prefix is 10 in 16^3, or about 0.25%. Finding a 0e... == 0e... collision has probability ~6e-6, if both inputs are random. The chance that two hashes collide in this way given N random inputs is 1-(1-p)^(N-1), for N>0.
The probability of generating a hash with the right prefix is 10 in 16^3, or about 0.25%. Finding a 0e... == 0e... collision has probability ~6e-6, if both inputs are random. The chance that two hashes collide in this way given N random inputs is 1-(1-p)^(N-1), for N>0.