aha! when we said it was going to be an 1 it was not an 1. when darkfire said it is not going to be an 1, it was an 1. so if we label our dice that we don't want the next number, it will be the next number.
EDIT: or maybe not.
Actually, it's a 1/46,656 chance of any 6 consecutive rolls of 1d6 being 123456 because of the following:
First roll: 1/6 chance of being a 1 Second roll: 1/6 chance of being a 2 Third roll: 1/6 chance of being a 3 Fourth roll: 1/6 chance of being a 4 Fifth roll: 1/6 chance of being a 5 Sixth roll: 1/6 chance of being a 6
Since all 6 of those events must be true for 123456 to occur, the probability is (1/6)^6, which is the same as 1 / 6^6, and 6^6 is 46,656. Here are the probabilities for completing this thread's goal with larger dice: