Blog post # 147:

(147 = 7 * 3 * 7.)

Amongst Bland Circumferences

Dissatisfied Glass

Counterintuitive Convexity

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

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

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

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.

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

(Did anyone read through this entire post?)

Leroy

## Sunday, January 2, 2011

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