Palindromia

Blog post # 147:
(147 = 7 * 3 * 7.)

Amongst Bland Circumferences


Dissatisfied Glass


Counterintuitive Convexity


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My goal appears today to be to scare away readers!
Only the coolest among us can withstand this trial by puzzles and poetry.

But first, something that is perhaps stupid, if not scary.

An advertising slogan for a 'palindromestic" cleaning-solution:

"Dirt? Egg? Get rid!"

-----------------------------

Speaking of palindromes...

Here is a puzzle. I don't know how many solutions there are, but there is at least one (plus its reflections).

Take an 8-by-8 grid, such as a chess board.
Place 8 stones on the board somehow, each stone in one of 8 different squares, such that there is exactly one stone in each column and exactly one stone in each row.

Make a list, called the "column list", of 7 numbers this way:
The mth number in the list is the number of rows difference, either upwardly or downwardly, between the stone in the mth column and the stone in the (m+1)th column. (m is an integer between 1 and 7.) So the mth number = the absolute value of the difference in the vertical coordinates between the stones in the mth (vertically running) column and the (m+1)th column (lined up left to right).

Make another list, called the "row list", of 7 numbers this way:
The mth number in the list is the number of columns difference, either leftward or rightward, between the stone in the mth row and the stone in the (m+1)th row. (m is an integer between 1 and 7.) So the mth number = the absolute value of the difference in the horizontal coordinates between the stones in the mth (horizontally running) row and the (m+1)th row (lined up top to bottom).

Now, the stones are placed in such a way upon the grid that:

*The first three terms of the column list form a palindrome.
*The last three terms of the column list form a palindrome.
*All seven terms of the column list form a palindrome.
(The middle condition above is redundant.)

*The first three terms of the row list form a palindrome.
*The last three terms of the row list form a palindrome.
*All seven terms of the row list do NOT form a palindrome.

*And, finally, the sum of the terms in the column list plus the sum of the terms in the row list is 48.

(Remember, all terms of the column list and the row list are positive, whatever the directions the stones are from each other.)

How are the stones placed?

Any solution that fulfills all of the requirements is considered valid.

As an example, here is a solution where the sum of the column list's terms plus the sum of the row list's terms is 45, but all conditions above involving palindromes are met:

. * . . . . . .
. . . . . . . *
* . . . . . . .
. . . . . . * .
. . * . . . . .
. . . . * . . .
. . . * . . . .
. . . . . * . .

The column list is:
2,4,2,1,2,4,2

The row list is:
6,7,6,4,2,1,2

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And if the numbers above didn't frighten you, the words below certainly will.

Two poems!
(Nooooo!)

Circumferences Around This Egg
---------------------

I will decline to describe
such circumferences
Around this imagined egg.
They are to be
As multitudinous straps
of varying widths but
Of uncounted finitudes.
They are to be quite
Aglow and, so, despised
by cloth and truth's
Antagonists screaming.
And this egg is
Plagiarized from randomness.
Yet it is made
Of mental metals
all existing clockwise. It is
Blasphemous as to its
glossiness. But it is
Poisonous in its hexagonality.
It
Is partially encased
in the wrap of
Introspection and scrawl.
It is enclosed
In an exoskeleton
surely weird and
Certainly within it.
Its shell is
Its dreams; and
its pulp is its reality. And
I will never explain
its visions shown unto me,
Despite the egg's
bland saltiness, that
Saltiness that is tasted
then sharply severed
From such circumferences
wholly demanding
And each unpurposeful.

------------------------------

Certainty Of Uncompleted Riddles
-------------------------

Yes, the certainty of
uncompleted riddles
Does confuse those grids
redrawn and reiterated.
It does confound my
selfish game of palindromes,
Palindromes marked within
their uniqueness, within
All columns and rows
of solitude, of singularity.

It does consider the
progression of differences
-- Halfway symmetrical,
wholly so again,
Yet perpendicularly
halfway reflected,
Wholly asymmetrical.
... Ah, quite
A tempting angularity
is drawn against
That diminutive minimization,
because it
Is multitudinous and
plurally distinctive.

Yes, the puzzle is implied
in every permutation
Upon those penciled edges
written with pen.
Yes, the thoughtful screams
of my inertia
Do contemplate these
configurations each
Scattered among
my own disregard. And I am
Neither adroit nor fulfilled
by such rectangles,
By such certainty unjustified,
such certainty
Un-alphabetically presumed,
surely, by my
Prideful and
mathematical questioning.

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(Did anyone read through this entire post?)

Leroy