When Do the Last 10 Days of Ramadan Start?
Question

I have a question that arose from something that one of my friends said about the last ten nights of Ramadan. My friend said: If Ramadan is twenty-nine days, then the last ten days are from the nineteenth to the twenty-ninth. So how can I know the odd-numbered nights among them? What is your response to that?
Praise be to Allah.The last ten nights of Ramadan begin from the night before the twenty first day, whether the month is thirty days or is twenty-nine days. 
This is indicated by the report narrated by Al-Bukhari  (813) and Muslim (1167) from Abu Sa`d Al-Khudri who said: The Messenger of Allah (blessings and peace of Allah be upon him) observed I`tikaf during the first ten days of Ramadan , and we observed I`tikaf with him. Then Jibril came to him and said: “What you are seeking is ahead of you.” So he observed I`tikaf during the middle ten days , and we observed I`tikaf with him. Then Jibril came to him and said: “What you are seeking is ahead of you.” So the Prophet (blessings and peace of Allah be upon him) stood up and addressed us on the morning of the twentieth of Ramadan and said: “Whoever observed I`tikaf with the Prophet (blessings and peace of Allah be upon him), let him come back, for I was shown Laylat Al-Qadr then I was caused to forget it. Verily it is in the last ten nights, on an odd-numbered night, and I saw myself prostrating in mud and water.” The roof of the mosque was made of palm leaves, and we had not seen anything in the sky, but then a cloud came and it rained, and the Prophet (blessings and peace of Allah be upon him) led us in prayer until I saw the traces of mud and water on the forehead of the Messenger of Allah (blessings and peace of Allah be upon him) and the tip of his nose, in fulfilment of his dream. 
According to a report narrated by Al-Bukhari (2027), the Messenger of Allah (blessings and peace of Allah be upon him) used to observe I`tikaf during the middle ten days of Ramadan. One year he observed I`tikaf until on the night of the twenty first, which was the night on the following morning of which he would come out of his I`tikaf, he said: “Whoever was observing I`tikaf with me, let him observe I`tikaf for the last ten nights, for I was shown this night then I was caused to forget it, and I saw myself prostrating in water and mud on the following morning. So seek it in the last ten nights, and seek it on every odd-numbered night.” It rained that night, and the mosque was ‘covered with palm leaves, so the mosque leaked, and I saw with my own two eyes the Messenger of Allah (blessings and peace of Allah be upon him) with traces of water and mud on his forehead, on the morning of the twenty-first. 
Al-Hafiz (may Allah have mercy on him) said: 
“This clearly shows that this speech was given on the morning of the twentieth day, and the rainfall occurred on the night before the twenty first.” (Fath al-Bari (4/257) 
According to a report narrated by Al-Bukhari (2018) and also Muslim (1167), it says: The Messenger of Allah (blessings and peace of Allah be upon him) used to stay in the mosque (for I`tikaf) in Ramadan, in the ten days in the middle of the month, then on the evening of the twentieth, before the twenty first, he would go back to his home, and those who had stayed in the mosque with him also went back home.
This indicates that the last ten days begin from the night before the twenty first. 
Hence the view of the majority of scholars – including the four imams – is that whoever wants to observe I`tikaf during the last ten nights of Ramadan should enter the mosque before sunset on the night before the twenty-first. 
The odd-numbered nights of the last ten are the nights before the twenty-first, twenty-third, twenty-fifth, twenty-seventh and twenty-ninth. 
The night before the nineteenth is not included among the odd-numbered nights of the last ten, regardless of whether the month is complete or incomplete (i.e., thirty or twenty-nine days), because it is one of the middle ten. 
Al-Hafiz Ibn Hajar (may Allah have mercy on him) said: 
“Laylat al-Qadr can only be in Ramadan, then in the last ten nights of it , then in the odd-numbered nights of those ten, not on any specific night among them. This is what is indicated by all the reports that have been narrated concerning it.” (Fath Al-Bari (4/260) 
And Allah knows best.