How could they believe their calendar was off by 6 days? Each month is either 29 or 30 days. Moshe erred 6 times (29 day months instead of 30 day months) from the previous Tisha B'AV ??? If so, they would have known it after 2 or 3 times since the full moon would not be on the 15th and the old moon and not the new moon would have been visible at the start of the month.
bernard dickman, brooklyn, ny
This question has bothered me for years, though in a slightly different format.
I don't think it was a matter of the past six months, since the Gemara in Rosh Hashanah says that even if Beis Din pronounced the wrong day Rosh Chodesh, that day is nevertheless Rosh Chodesh.
In that case, they must have thought that they erred regarding that very Rosh Chodesh Av by six days - which is no less incomprehensible.
I don't have a real answer to the question, but the following two points ought to alleviate the problem somewhat.
Firsly, bear in mind Rabeinu Bachye, who claims in Parshas ha'Chodesh that they never saw the New Moon in the Desert, since they were perpetually covered by the Clouds. As a matter of fact, he asserts that Kidush ha'Chodesh took place according to the reckoning and not by sighting (I have a number of questions on this proof, but that is what he says).
Secondly, every year, fifteen thousand (out of the six hundred thousand people who were destined not to enter Eretz Yisrael) died on Tish'ah b'Av. This was the fortieth year, and the last batch of fifteen thousand had to die, as per Hash-m's decree. Remember, Hash-m had said nothing about the decree being rescinded, so when the day of Tish'ah be'Av dawned, and it was discovered that all fifteen thousand people were still alive, they figured that either (Kevayachol) Hash-m had erred or they had. Knowing that Hash-m does not make mistakes, they concluded that, feasible or not, they must have somehow miscalculated. And so, night after night, they entered their graves again, until the fifteenth day arrived and they knew that they could not possibly have erred, and that Hash-m had indeed rescinded the decree.
Wishing you a Kesivah va'Chasimah Tovah