>>8980972It is precisely exactly D4.

Albert knows that Bernard does not know which is the correct pad. Therefore, B5 and A6 are eliminated as possibilities. For if B5 or A6 were the correct pads, then Bernard would have known what the correct pad was, since those are the only pads on paths 5 and 6, respectively.

Bernard, beforehand, didn't know which was the correct pad. However, he now knows that Albert did not know the correct pad. Albert, however, also knew that B5 and A6 were incorrect. This means that B4 is not the correct pad, since if Albert had the letter B, he would have known the correct pad to be B4, since the only other pad on B, B5, is known to be false by dint of Bernard not knowing the correct pad.

Bernard then states "but now I know". The only way he would know the correct pad is if he had the number 4, since 5 and 6 both have no correct pads, 4 has one pad inferred above to be incorrect (B4), with only one remaining (D4), and paths 1,2, and 3 each have 2. The only way for Bernard to know now is for his number to be 4. Albert realizes this and also knows that D4 is the only option.