Where is Tuvalu? 2.0

 

Sometime back I wrote this post: Where is Tuvalu?

https://hunterfiftyfour.blogspot.com/2025/05/where-is-tuvalu.html

Now, there is news that Tuvalu may well cease to exist altogether. Will be obliterated from the face of the earth. Watch this video:

https://youtu.be/ggV9Xfodl08?si=L2EWqoKzoGz82VEx

Not tethered with puppeteer's string or whim

 

The kite's final resting place

Is among the branches of a tall tree,

It was too tired for being given rope,

Then reeled in when flying free.

Now, it is not tethered 

With the puppeteer's string or whim,

But is open to the elements,

And, that is not a small thing.

Knight's tour on a chessboard from ancient Sanskrit text: 2

 

This post is a follow up on my previous post:

https://hunterfiftyfour.blogspot.com/2025/12/knights-tour-in-chessboard-from-ancient.html

In the Comments section Dilip asked me to give more examples through diagrams on the Chitrabandh Shlokas. Although some Chitrabandh Shlokas have been given in the IIT resource link, it may be prudent to believe that most of us would not go into the contents given in that link. I therefore give a walk through some relevant pages given in the book whose cover is here (also present in the IIT resource link):

The Shlokas 19 and 20 in this Kavyamala 92 are the knight's tour on a 4x8 chessboard. Here is an image of the page where these two Shlokas are printed:

Chess knight circuit (G. S. S. Murthy's Translation) of the Shlokas:

Sthiraagasaam sadaaraadhyaa vihataakatataamataa| Satpaaduke saraasaa maa rangaraajapadam naya||

Sthitaa samayaraajatpaagataraa modake gavi| Duramhasaam sannataadaa saadhyaataapakaraasaraa||

The author beseeches the sandals of God to help him reach the abode or the feet of God. The two slokas together form one sentence.

Sat+paaduke = O Sandals of Brahma,

Sthira+aagasaam, Sadaa+aaraadhyaa = (you are )always revered by the worldly who are confirmed sinners,

Vihata+aka+tata+amataa = (you are) the destroyer of unhappiness and instruments of unhappiness,

Saraasaa = (you are) always accompanied by (the jingling) sound (of trinket bells attached to the sandals?)

Maa, naya = take me,

Rangaraaja +padam = to the feet or abode of God.

Samaya+ raajat+paa = (you are ) the protector of those shining through their good conduct,

Aagata+raa = (you have) attained brilliance of gold,

Modake = (you) dispense joy,

Gavi, sthitaa = (you) are at the center of sun,

Durahmasaam, sannataa+daa = (you are) destroyer of the despondency of the wicked,

Saadhya+ataapa+karaa = rays (of your gems) have the power of removing the heat (of the devotee),

Aasaraa = (you) move all around,

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Shlokas 19 in row and column form. Numbers written is squares to indicate how to derive Shloka 20 from 19 by legit knight moves:

Other shlokas in the IIT resource are here:

https://www.iiitb.ac.in/Ganaka/projects/paduka/padukaaslokas/1.jpg

https://www.iiitb.ac.in/Ganaka/projects/paduka/padukaaslokas/2.jpg

https://www.iiitb.ac.in/Ganaka/projects/paduka/padukaaslokas/3.jpg

https://www.iiitb.ac.in/Ganaka/projects/paduka/padukaaslokas/5.jpg

https://www.iiitb.ac.in/Ganaka/projects/paduka/padukaaslokas/6.jpg

Other chitrabandh examples given in IIT resource:

https://www.iiitb.ac.in/Ganaka/projects/paduka/padukapictures/p1.jpg

Shlokas 16, 17, and 18 in chitrabandh:

https://www.iiitb.ac.in/Ganaka/projects/paduka/padukapictures/p2.jpg

One interesting example in the IIT resource of deriving another Shloka by reading the given Shloka in reverse . Here, Shloka 77 is derived from Shloka 76 by reading Shloka 76 in reverse. This is from Dandin:

https://www.iiitb.ac.in/Ganaka/projects/paduka/dandin/1.jpg

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Knight's tour on a chessboard from ancient Sanskrit text

 

My friend Dilip Ranade forwarded the above video along with the following write up:

The video shows a solution to the problem of a knight moving to all squares of a chess board without repeating a square. 

Amazingly, solutions for the same have been found in Sanskrit classics!

Here is a link to a short paper available in an IIT site:

https://www.iiitb.ac.in/Ganaka/projects/paduka/paduka.html

Here is an elaboration of the theme of the knight's move to cover all squares in a 4x8 chessboard exactly once as derived from ancient Sanskrit Shlokas. Research tells us that there is a Chaturanga-Turanga Bandha corresponding to Śhlokas 19–20, found on page 392 of the Paduka-Sahasram edition.

This is the famous knight’s-tour shloka.

What “Chaturanga-Turanga Bandha” Means:

Chaturanga = chess (the four-limbed ancient Indian game)

Turanga = a horse

So, Turanga-bandha = “the horse-pattern” → in chess this means the knight.

Thus this bandha (poetic figure) is a verse arranged exactly like a knight’s tour on a modified board.

Why This Shloka Is the Knight’s Tour:

In this bandha:

The poet writes a Sanskrit verse.

He then splits the verse into syllables.

Each syllable is placed in one square of a grid.

The squares are numbered.

The numbers show the order in which a knight can visit all squares without repeating any. This is the Hamiltonian path problem on a chessboard. Because the pattern involves a chess-knight (turanga), the shloka is named 'Chaturanga-turanga-bandhaḥ — the chess-knight pattern.'

Here is the Shloka 19:

And, this is how the arranged with syllables in row and column grid by the poet:

The syllables in English letters and the numbers in Roman numerals would be the following table:

How the knight’s movement is used:

As we can see, the squares of the board are arranged in a 4 × 8 rectangle. And each syllable is placed in order row wise. If you read left to right, row wise, you get the Shloka (written in Devnagri)given above. The above matrix gives the sounds of the syllables in English and the numbers in Roman numerals.

If you follow the numbers in the diagram:

1 → 2 → 3 → … is a legal knight move each time. You will cover all 32 squares exactly once. The syllables of the shloka are placed in an order that corresponds to a knight hopping from one square to the next. The syllables of the shloka are placed in an order that corresponds to a knight hopping from one square to the next.

Reading the syllables in that order reconstructs the full shloka. And below is Shloka 20 that has been created by knight's legit moves across the board, and touching each square only once:

And here is the move of the knight to create the above Shloka number 20:

This is a constrained combinatorial construction. The poet must choose a verse whose syllables can be arranged so that the knight's path is possible.

Why this s combinatorially really amazing:

Knight tour of duty are nontrivial. Finding a knight’s tour (even on a 4×8 board) is a known combinatorial puzzle. But here, the poet must also place syllables. He must arrange metrical structure, meaning, and the knight's Hamiltonian constraint simultaneously.

Are there more than one way that the knight could move?

Yes — mathematically, there are many possible knight tours on a 4×8 board. But only one tour matches the syllable order that reconstructs the shloka.

Heavy to pull the chain

 

When no one calls you back

To get off the train,

When the platform goes empty,

It's heavy enough to pull the chain.

Silicone street

 

Hearts in this town

Are made of glass,

And when some break,

They go to shards.

Don't go barefoot 

On the grass,

For your feet may bleed,

With the broken glass.

Glass and shards everywhere,

On this lonely silicone street,

Walk but with heavy boots,

And crush glass 'neath your feet.

Heart: do you want another cut?

 

For wounds that just do not heal,

For wounds that are but a feel,

Surgeons often pare another wound,

Near where such a wound was found,

That both wounds in tandem,

Grow chrysalis, and heal together.

Heart, shall we go through this rut?

Do you want another cut?