Did this month's question start on March 31st? Not April 1st?

After they had finished questioning the first witness, they would bring in his partner and question him in similar fashion. That day, the thirtieth day, was now declared Rosh Chodesh of the new month. The head of the Sanhedrin would proclaim: “Mekudash!” (“Sanctified!”) and everyone would respond, “Mekudash!

The previous month was now retroactively determined to have had only twenty-nine days. The following night (the second night of the month), huge bonfires were lit on designated mountaintops. Lookouts stationed on other mountaintops would see that a fire had been lit, and would light their own fires.

This chain of communication led all the way to Babylonia, so that even very distant communities knew that the day beforehand had been declared Rosh Chodesh. Eventually, the Sadducees12 started lighting fires on the wrong days in order to manipulate the calendar. To prevent this confusion, the fire-on-mountaintop method of communication was discontinued, and instead messengers were dispatched to Babylonia and all other far-flung Jewish settlements.

This took a lot longer, a delay which had (and still has) halachic implications with regards to observance of the second day of holidays in the Diaspora. Members of the Sanhedrin would go to a highly visible location, where they would partake in a celebratory meal to signify the new month. No fires were lit that night.

The new month is always either on the 30th or 31st day; if they hadn’t lit fires the night before, it was understood that the new month started on the 31st day.