A chess puzzle that is also a hymn.

Around 1300 CE, Veṅkaṭanātha, remembered as Vedānta Deśika, composed the Pādukāsahasram: 1,008 verses in praise of the sandals of Raṅganātha at Śrīraṅgam. Chapter 30, the Citra Paddhati, holds these two 32-syllable anuṣṭubh verses.

929, the sequential reading

स्थिरागसां सदाराध्या विहताकततामता ।
सत्पादुके सरसा मा रङ्गराजपदं नय ॥

sthirāgasāṃ sadārādhyā vihatākatatāmatā / satpāduke sarasā mā raṅgarājapadaṃ naya

A prayer to the sandals: lead me, ever worthy of worship, whose feet are unshaken, to the feet of the king of Raṅga.

930, the knight's-tour reading

स्थिता समयराजत्पागतरामादके गवि ।
दुरंहसां सन्नतादा साध्यातापकरासरा ॥

sthitā samayarājatpāgatarāmādake gavi / duraṃhasāṃ sannatādā sādhyātāpakarāsarā

The same 32 syllables, read in the order a chess knight visits the squares of a half-board. Both verses are metrical, grammatical and devotionally meaningful.

Chaturaṅga-turaṅga-pāda-bandha

“Binding by the foot-step of a chess-knight.” Verse 929 is laid on a 4×8 half-chessboard in row-major order, one syllable per square, matching anuṣṭubh's four pādas of eight. The small number in each cell is that syllable's position in verse 930's tour.

Step through the tour

1स्थि

30रा

9ग

20सां

3स

24दा

11रा

26ध्या

16वि

19ह

2ता

29क

10त

27ता

4म

23ता

31स

8त्पा

17दु

14के

21स

6र

25सा

12मा

18रं

15ग

32रा

7ज

28प

13दं

22न

5य

Three lenses

Graph theory
A Hamiltonian path
The 32 squares form a graph in which knight moves are edges. The tour visits every vertex once. The Sanskrit fixes which of the many possible paths is used.
Poetics
Two readings, one set of syllables
Each verse has four pādas of eight syllables. The first is read normally; the second is the same syllables reordered by the path, and it still scans.
Devotion
Constraint and grace
The chess-puzzle form matches the theme of the verses, which treat the world as a play of constraint and grace.

The achievement is a joint constraint: the permutation must be a Hamiltonian path on the knight graph, the reordered syllables must scan as anuṣṭubh, and the result must be grammatical and devotional.

Lineage

Author, work	Date	Board	Syllables	Subject
Rudraṭa, Kāvyālaṅkāra 5.15	c. 850 CE	4 × 8	32 + 32	Poetic ornament
Ratnākara, Haravijaya ch. 6	c. 850 CE	4 × 8	32 + 32	Hymn to Śiva
Vedānta Deśika, Pādukāsahasra 30.40–41	c. 1300 CE	4 × 8	32 + 32	Praise of Raṅganātha's sandals
Euler, Solution d'une question curieuse	1759 CE	8 × 8		First Western analysis

Rudraṭa and Ratnākara are the earlier Kashmiri instances; Deśika is the synthesis. Tradition says the Pādukāsahasram was composed overnight; that is tradition rather than established fact.

References