Turagagati method for 4 × 4 pandiagonal magic squares by Nārāyaṇa Paṇḍita

The pandiagonal magic squares have been known in India from the time of Nāgārjuna (c.100 CE) and Varāhamihira (c.550 CE). In his comprehensive mathematical study of magic squares presented in the Bhadragaṇita chapter of Gaṇitakaumud\(\bar{\iota }\) (c. 1356 CE), Nārāyaṇa Paṇḍita has briefly outlined a method for constructing 4 × 4 pandiagonal magic squares based on turagagati or horse movements in a chess board. In this paper, we present a study of the verses of Nārāyaṇa Paṇḍita which leads to a method of construction of 4 × 4 pandiagonal squares by horse moves only. We also show that this algorithm generates all (and only) the 384 pandiagonal squares of order 4. Besides presenting this algorithm, this paper discusses various properties exhibited by these squares along with their proofs.