Responsa for Rosh Hashanah 3:8
אמר מר מלך שעמד בעשרים ותשעה באדר כיון שהגיע אחד בניסן עלתה לו שנה הא
he is reckoned to have reigned a year. If on the other hand he ascended the throne on the first of Nisan, he is not reckoned to have reigned a year till the next first of Nisan comes round. The Master has said, 'If a king ascends the throne on the twenty-ninth of Adar, as soon as the first of Nisa arrives he is reckoned to have reigned a year.'
Teshuvot Maharam
You asked about a community that wished to declare a fast on Monday, Thursday and Monday, and the first fast day fell on Tu Bishvat. Should they be concerned and postpone the fast to the following week or not? Thus my inclination is that the fast should be postponed to the following week, and the fast should not be set because we do not find any fast on Rosh Hashanah.
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