Reference: al-Ajwibah wal-Buhooth wal-Mudaarasaat – p446, no.535
Sharh Masaa.il al-Jaahiliyyah
Question: How are we to understand the Prophet (sal-Allaahu ‘alayhi wa sallam) encouraging ‘Abdullaah ibn ‘Amr al-’Aas (radhi-yAllaahu ‘anhu) with the fast of [Prophet] Daawood (‘alayhis-salaam), whilst he himself did not fast it despite it being the best of fasts?
Response: This [advice] was because of the strength of ‘Abdullaah ibn ‘Amr al-’Aas (radhi-yAllaahu ‘anhu); he was a strong young man, and liked to fast a lot. So the Prophet (sal-Allaahu ‘alayhi wa sallam) advised him with the best of fasts – and that is the fast of Daawood (‘alayhis-salaam) – that he fasts every other day.