Combinatoric's Traces in Shiite Jurisprudence

Shahīd-i ʾAwwal is one of the great jurists of 14th century AD. His works are still part of the Islamic seminaries’ curriculum. One of his most famous book is Ghāyat al-Murād, which includes several topics on Islamic law. One of these topics is the problem of the daily prayers which have not been done at they proper time and ought to be done again. The solution of that problem needs some knowledge of mathematics, especially combinatorics. It is necessary prayers exactly in the same sequence as the original prayers. Shahīd-i ʾAwwal has solved the problem by inventing a mathematical method, the function that is called today Factorial. Other great jurist, Shahīd-i Thānī, also has solved the problem, but not exactly in the same way. He wrote a commentary on Shahīd-i ʾAwwal’s Lomʿa. There is no doubt that the concept of this function is well understood.