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Saturday, January 16, 2016

Rudrata and his Knight’s move verse: An interesting feature

Rudrata and his Knight’s move verse: An interesting feature

Rudrata has given the following verse as an example of Knight’s move picture-verse:
सेना लीलीलीना नाली लीनाना नानालीलीली ।
नालीनालीले नालीना लीलीली नानानानाली ॥ १५ ॥
If we enter this into half of a chess board ( 8columnsx4 rows) serially one character in each cell, the knight’s move sequence of steps which visits each cell once and once only results in another meaningful verse. This sequence is cryptically given in a meaningless verse by the commentator Namisadhu (See my previous blog at http://gssmurthy.blogspot.in/). Rudrata’s verse is shown entered in a 8x4 chess board below:
se-1
naa-30
lii-9
lii-20
lii-3
naa-24
naa-11
lii-26
lii-16
naa-19
naa-2
naa-29
naa-10
lii-27
lii-4
lii-23
naa-31
lii-8
naa-17
lii-14
le-21
naa-6
lii-25
naa-12
lii -18
lii-15
lii-32
naa-7
naa-28
naa-13
naa-22
lii-5

The numeral in each cell is the serial number in the knight’s move sequence.
In this particular example given by Rudrata the knight’s move sequence gives the same verse, which in general, for a Knight’s Move Verse, is not true.  Verses constructed by Bhoja and Vedanta Desika yield different meaningful verses.
It is also to be noted that Rudrata uses only 4 distinct akshara’s in his verse.
It is natural to investigate if his use of only 4 distinct aksharas is connected with the Knight’s Move sequence yielding the same verse. It indeed turns out that in order that the Knight’s move sequence yield the same verse, there cannot be more than 4 distinct aksharas in the verse.
We set up a Table of equality where the 2 serial cell-numbers in a row have to be the same akshara as follows:

Main verse
Knight's move verse
Cell No.
Cell No.
1
1
2
11
3
5
4
15
5
32
6
22
7
28
8
18
9
3
10
13
11
7
12
24
13
30
14
20
15
26
16
9
17
19
18
25
19
10
20
4
21
21
22
31
23
16
24
6
25
23
26
8
27
14
28
29
29
12
30
2
31
17
32
27
The above Table of Equality leads to the interesting result that
1.   the following cells have to have the same akshara:
2,11,7,28,29,12,24,6,22,31,17,19,10,13,30.

2.   The following cells have to have the same akshara:
3,5,32,27,14,20,4,15,26,8,18,25,23,16,9,

3.   Cell no.1 and Cell No.21 can have distinct aksharas.
Rudrata’s verse adheres to the above criteria where cell No.1 contains akshara ‘se’, cell No.2,11 etc contain akshara ‘naa’, cell No.3,5 etc contain akshara ‘lii’ and cell no.21 contains akshara ‘le’.

As a matter  of curiosity when a condition is imposed that the Knight’s move verse be the reverse of the main verse, it turns out that all the cells have to have the same akshara which of course is trivial.

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