Chaturanga Turanga Bandham - चतुरङ्ग तुरङ्ग भन्धं

 SUBHASHITHANI:571

The 44th chess olympiad is being played in Tamil nadu. So, I thought appropriate to mention about an old chess problem known as'Knight's tour problem'. It is said many mathematicians like Euler (1707)and a few others couldn't find a solution, Sri vedanta Desika( 1268)describes the moves through two verses in Paduka sahasram. 

The knight's tour problem:

The earliest known reference to the knight's tour problem dates back to the 9th century AD. In Rudraṭa's Kavyalankara, a Sanskrit work on Poetics, the pattern of a knight's tour on a half-board has been presented as an elaborate poetic figure (citra-alaṅkāra) called the turagapadabandha or 'arrangement in the steps of a horse'. The same verse in four lines of eight syllables each can be read from left to right or by following the path of the knight on tour.

The Sri Vaishnava poet and philosopher Vedanta Desika during the 14th century in his 1,008-verse magnum opus praising Lord Ranganatha's divine sandals of Srirangam; i.e., Paduka Sahasram (in chapter 30: Chitra Paddhati) has composed two consecutive Sanskrit verses containing 32 letters each (in Anushtubh metre

)

 where the second verse can be 

 from the first verse by performing a Knight's tour on a 4 × 8 board, starting from the top-left corner.

 The transliterated 929th and 930th verse is as follows:

sThirAgasAm sadhArADhyA vihathAkathathAmathA
sathpAdhukE! sarAsA mA rangarAjapadham naya II 929.
sThithA samayarAjathpA gatharA mAdhakE gavi
dhuranhasAm samnathAdhA sAdhyAthApakarAsarA II 930.

 

Sthi 1	rA 30	Ga 9	sAm 20	Sa 3	dhA 24	rA 11	dhyA 26
Vi 16	Ha 19	thA 2	Ka 29	Tha 10	thA 27	Ma 4	thA 23
Sa 31	thpA 8	Dhu 17	kE 14	Sa 21	rA 6	sA 25	mA 12
Ran 18	Ga 15	rA 32	Ja 7	Pa 28	Dha 13	Mna 22	Ya 5

# Follow the numbers in the square from 1 to2, then 3,  ...32. It will trace the movement of a horse in a chess board; without the horse being in the same square twice.

SlOkam 929 and 930

These two slOkmas are to be read together as one set.
This chithra bhandham is known as " Chathuranga-Turanga 
padha bhandham ". Chathurangam means a chariot and 
Turangam means a horse. These two slOkams fit like 
a horse-drawn carriage as a unit. The verse moves like 
the steps of a horse drawing the chariot. The geometric 
representation of the first verse and its relationship (symmetry)
to the subsequent verse shows the Turanga Padha kramam .
The 32 aksharams have to be presented in a 8x4 mode 
to appreciate this kramam (sequence).

There are 32 aksharams in the slOkam 929 as well as 

in sLokam 930. One has to position the 32 aksharams of
the first slOakam in four rows and follow it up with the 32
aksharams of the second slOkam in the same manner.
Then one has to use the movement regulations of a horse 
in the chess game ( chathurangam ). 

SRI KRISHNAYA THUBHYAM NAMAH

Ps: 1.The meaning of the slokas are not included to retain brevity.

2. Sri vedanta desika lived six hundred years before Euler.