Bhishma astami is celebrated on Magha Shukla Astami as the day he departed. However Mahabharata says:
O Yudhishthira, the lunar month of Magha has come. This is, again, the lighted fortnight and a fourth part of it ought by this (according to my calculations) be over.
māgho 'yaṃ samanuprāpto māsaḥ puṇyo yudhiṣṭhira tribhāgaśeṣaḥ pakṣo 'yaṃ śuklo bhavitum arhati
Why it's Astami when it's said a fourth part of the Paksha which comes to 3-4 days?