The knight's tour problem

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 1/

33

Index - Tens: 01 The problem is having a knight traverse across all squares on a chessboard without visiting any square twice. The Padhuka Sahasram by Sri Vedanta Desikan presents a solution to the problem in verses 929 & 930. The first verse is written sequentially and the next is read along the path taken by the knight yielding the result.929. sThirAgasAm sadhArADhyA vihathAkathathAmathAsathpAdhukE! sarAsA mA rangarAjapadham naya930. sThithA samayarAjathpA gatharA mAdhakE gavidhuranhasAm samnathAdhA sAdhyAthApakarAsarA

Translation by U.Ve. Dr. V.N. Vedanta Desikan Swamin:

Oh Paaduka of the Lord who is meant by the word 'Sat'! The worst of

sinners can worship You and benefit. You ward off all evil

happenings, which are inherently grief-causing. What a melodious walk

You possess! You diligently keep guard in respect of people who stick

to the righteous path with pure activities. You remain in an

effulgent site with SRI, unique to You, granting affluence to the

worshippers. You remove the pitiable condition that accrues to

sinners. You make the strolls pleasing and relaxing to the Lord, when

He has to go out. May You please lead me on to the Lord Ranganatha's

Abode!

Special Notes by V.Sadagopan(V.S):



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 ). That movement is

to jump to the next position and from there gallop to

the end of the diagonal posiiton ..



1) UtthamUr Swamy's anubhavam( SlOkams 929 & 930):

Oh Holy Paadhukais of the Lord ! Please bring me close to

Lord RanganAthA's sacred feet ! You are the pair to be worshipped

always by those burdened down by their bundles of sins .

You destroy their sorrows . You are celebrated for that blessing .

You have a delectable sound , when You move about.

You protect the righteous. You are rich in wealth and attributes.

You reside inside the rays that produce joy. You destroy the sorrow

of those , who have committed heinous sins .Your movements

banish the afflictions suffered by the above . May You bring Your

Lord's feet to me or take me to where they are !



2) SrImath Andavan's anubhavam(SlOkam 929) : Oh Sath PadhuE !

You are the one fit to be worshipped by SamsAris in this world and

to be recognized as the PurushArTam in the other world (during

the stage of Mukthi) . You accept the Prapathti performed to You

and destroy sanchitha and PrArabdha karmAs of the prapannAs

and grant them Moksham . My prayers to you are to bless me

quickly with the attainment of the access to Your dear Lord's

sacred feet in Parama Padham .



(3) SlOkam 929/ Oh Sath-PaadhukE ! ( the Paadhukais of Parabrahmam )!

SamsAris have unquenchable sins ( sTira aagasAm) . For such

nithya samsAris , You are the fit object of worship ( sTira aagasAm

sadhA aarAdhyA ). Oh glorious Paadhukais which remove

inauspiciousness ( viahatha aka tathaa amathaa ) and have

the pleasing naadham ( saraasA ) ! Please lead me to

the sacred feet of Your Lord ( Maa RangarAja padham naya) .



4) SrImath Andabvan's anubhavam: (SlOkam 930) :The PaadhukAs have

the following attributes and the prayer to the Paadhukais is to connect

the samsAri to the sacred feet of the Lord at SrI Vaikuntam :



(a) It protects the righteous , who do not slip from their sath-

SampradhAyam through the power of their austerity .



(b) It has all the Iswaryams under its control and distributes them

according to its desires to aasrithAs .



(c) It becomes a fit object for dhyAnam as it sits in the middle of

its brilliant rays as a JyOthirmaya vasthu that gladdens the

heart of all beholders .



(d) It removes all the fierce sins of samsAris , the moment they pray

to it for protection through the contact with its lustrous rays .



(e) It has the power to travel to all corners of the world to banish

the sorrows of those , who seek its protection .



5) The sacred PaadhukAs of the Lord protect those who shine

with their observance of the Sath-sampradhAya anushtAnams

and ask those PaadhukAs to lead Swamy Desikan to

the sacred feet of Lord RanganAtha (Samaya Raajath Paa ThvAm

Maa RangarAja Padham naya ) . Other attributes of the PaadhukAs

qualifying them to lead Swamy Desikan to the sacred feet of the Lord

of SrIrangam are next described : (a) It is the possessor of parama

Iswaryam ( aagatha raa ) (b) it stays in the middle of Soorya MaNDalam

in an auspicious state resplendent with its own jyOthi ( MaadhakE gavi

sTithA), (c) It destroys the fierce sins of samsAris and grants them

an auspicious state ( dhuramhasAm sannathA dhaa) , (d) it has

the tranquil and cool rays that travel everywhere ( Saadhya atApa kara

aasArA). May Thou lead me to the closeness of Your Lord ( Thvam

Maa RangarAja paadham naya )...(V.S).