I say, and with God's success: There are five rulings related to tayammum: First: Tayammum is valid after the time of prayer has entered and before it: because the dust is universally permissible; as narrated by Abu Dharr  who said that the Prophet  said: "Indeed, pure soil is the purification of a Muslim for even ten years, and when he finds water, he should touch his skin with water," in Sahih Ibn Hibban 4: 139, Musannaf Ibn Abi Shaybah 1: 144, Musnad Ahmad 5: 146, Sunan Al-Daraqutni 1: 187, Sunan Al-Bayhaqi Al-Kubra 1: 187, and Ibn Al-Qattan authenticated it. Second: He can pray with tayammum as much as he wishes from obligatory and voluntary prayers: because the hadith: "Indeed, pure soil is the purification of a Muslim..." is explicit that tayammum is a form of purification: that is, it purifies like ablution, and this is supported by Allah's saying after mentioning ablution, washing, and tayammum: {Allah does not intend to make difficulty for you, but He intends to purify you and complete His favor upon you that you may be grateful} Al-Ma'idah: 6, where it is mentioned in the context of gratitude for ablution, washing, and tayammum all together, thus it is explicit that tayammum is also a purifier like ablution and washing, so the three share in this, and if it were not so, it would have been mentioned with purification only after ablution and washing. Third: It is valid for him to perform tayammum after seeking water from someone who denied him: even if he prayed after being denied and then was given water by the one who denied him, the tayammum is invalidated only now, and he does not have to repeat what he has already prayed. Fourth: It is valid for him to perform tayammum if he is overwhelmingly certain of being denied by someone who has water: and it is not valid if he is overwhelmingly certain of not being denied if he asks for it; because he asked in a place where water is scarce, thus it would be usually available. Fifth: It is recommended for one who hopes to find water and is overwhelmingly certain of finding it to delay his prayer until the end of the time: but if he prayed with tayammum at the beginning of the time, then found water while the time remains, he is not required to repeat the prayer. However, if he does not hope for water, he should not delay the prayer from the beginning of the time; because the benefit of waiting is the possibility of finding water, so he performs it with the two complete purifications, and here it was not available; as narrated by Ali  who said: "If a man is in a state of major impurity while traveling, he should wait until the last part of the time, and if he does not find water, he should perform tayammum and pray," in Sunan Al-Bayhaqi 1: 233. Refer to: Sharh Al-Wiqayah p.112, Al-Bahr Al-Ra'iq 1: 163-164, Ghinayat Al-Mustamli p.69, and Rad Al-Muhtar 1: 167, and Allah knows best.