Let there be Six

Six Hexagons "Perfect" Connected

112723 1534 - Is the date and time now.

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OK - time to shift things around here because this is going to be a very serious mathematical post dealing with this hexagon puzzle I been wrestling with in my mind for well over a year now. So, tis time for some edits:

Please refer to this article for background information:

Now - from earlier….

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One edit deserves another…

Shapes 2-dimensionsal need to be understood for what they are without regard to orientation if you want to get a Grade of A in Geometry!

!!!

Time for choices to be made:

This is a clue one time given….take it or leave it I reckon.

…..some of us r sick of em, just like justice must be served

You can count on it!

~ I’ll figure out the shapes, but in the mean time - consider free will - and U choose! ~

You choose what you want.

~

This is a placeholder for the proof definitive that will be here easily understood and worked out with deliberation and determination after stretching after the reckoning I reckon.

Here is a taste of it - Shape #1 with 5 starting - in a row:

This starts it out - this post is going to be most precise in time.

Now - for the sake of the Buffalo Bills - fighting for their playoff hopes against the Eagles, the game is tied 31 all, I’ll post the next shape, but rest assured no matter how the game ends I’m gonna get the answer with six shapes for sure - and I suspect the answer is prime….

Not kidding around…

~~~~~ the time is 112723 1928 ~~~~~~

Here is shape #2:

Now - that adds 12 new shapes and that is only the 2nd shape with 4 in row and one off to the side - that is Shape #2 with 5 and it gives 12 new shapes with 6 being it was the 2nd shape considered.

~~~~~~ is is now 112723 2133 ~~~~~~~

~~~ is is now 122123 755 ~~~I’ve corrected two errors below for the 3rd and 4th shapes ~~~

here is the 3rd shape with six tiles each - seven new shapes - now the total is 23.

~~~~~ the time is 112723 2151 ~~~(note: error corrected on 122123)~~~

Here is shape #4:

So that completes the first four shapes with 5 tiles that started with “4 in a row” with a 5th tile added to get to the starting positions prior to adding a 6th tile hexagon perfect in shape hypothetically - and seems sort of ironic being there are 23 shapes total to get through, but now there are already 25 shapes with the 6th tile just looking at the initial shapes with a 5th tile that had four in row!

Of course, all work will be checked for accuracy and once I get through all 23 shapes I will prove the number of shapes with 6 hexagons perfect (in imagination) - I suspect it is gonna be either 89, 97, or maybe 101…..cause I already ran the numbers and made comparisons and I’m expecting the final number with six tiles connected 2-dimensionaly discreetly to be prime in nature.

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tis 112823 1602

Here is the next “origin” shape to be explored in detail:

(recall the first shape was 4 in a row)

Now this shape with 4 tiles, resulted in the following shapes with 5 tiles discrete….so tis a simple matter of 1 by 1 going through each of the 9 new discrete shapes not redundant with ones already dealt with above, below; adding a 6th tile, checking for “redundancy” and then getting a count. For the “new” shapes with six hexagons perfect in imagination.

I’ll tell a methodology for assessing redundancy quick and easy - if any potential “new” shape being considered has four (4) tiles in a row - odds are it ain’t new but is already indicated above previously with all the other shapes that have 4 in row by definition.

So - per the “nomenclature” Shape 2a will form the “#5 shape(s) with six tiles total”, Shape 2b, will be #6 shapes, shape 2c will be the #7 shapes…and so on and so forth. Here is the thing - there were 23 shapes total with 5 tiles and there are 9 shapes below and I’ve already assessed 4 shapes above, so after I finish with these ones below - one at a time (#5, #6, #7….#13) I will be well past half-way done for six tiles total and the further along I proceed the more precise the final number becomes, and the more this is done the more accurate predictions can be made for even “higher” numbers….

Moreover - if you want to have some serious math fun consider assessing the initial shapes in different orders and then see how many you get as your progress through the 23…..at the end no matter the order, the total number will be fixed and a whole and as I’ve gone on record stating - I suspect it will also be a prime number, and if this is the case, then a trend is forming and I’d be interested in the “proof on that”, but lets not get ahead before the count is official I reckon.

~

Tis 112823 1643 - just got off the phone with my wife, but here is Shape #5 (with six tiles):

~~~~~~~ tis 112823 1934 ~~~~~~~

the shapes keep coming - here is Shape 6:

~~~~~~ tis 112823 2009 ~~~~~~

I’ll admit - this is getting a bit “tricky” now in a way, but not a bad way, but I think I might need to “sleep on these” shapes swirling around in my mind - but with that said - here is Shape #7

Hey - if you see any redundant shapes in the 49 presented so far - please post a comment to that effect if you don’t mind…meanwhile, I’m gonna let it rest for a bit and I’ll be back with the other shapes but as for the total number of shapes - there is a good chance “we” are halfway there already…..and think about it - it is harmless shape imagination…..

~~~~ Guten Nacht ~~~~~~~~

******* ~~~~~~ tis 113023 919 ~~~~~~ *******

Well, I’ve “made it through” the first seven shapes and please don’t be distracted by the “2a - 2i” shapes in the image most close above versus the “2a - 2l” shapes in the image closer to the top. I could differentiate them, but it ought be evident one has shapes with five hexagons whereas the other has shapes with six hexagons. One had 9 “new” shapes and other 12, respectively - and no matter what “base shape” is considered, the one considered 2nd will normally offer up many new shapes, so that aspect of consideration has an element of randomness to it, but the bottom line is as follows:

There are a finite and fixed whole number of shapes made with any given number of hexagon tiles connected 2-dimensionally without consideration for orientation - so it really doesn’t matter the order they are examined

Not kidding around.

OK - let me make a needed “interruption” here:

So you have this:

It supposedly means this:

Felicitous is an adjective most often used in formal speech and writing to describe something that is very well expressed or suited for some purpose or situation. It can also be used as a synonym for pleasant or delightful.

~

Not kidding around still - I mean serious business in 2024

But before we make it to 2024 I’m gonna have to edit and finish this post about six shapes on a 6-sided “perfect” shape known in the vernacular as a hexagon.

Hexagons are in my head.

~~~ edit 12123 1550 ~~~

My guess is there are going to be some “errors” in this presentation, but the act of presenting it will make that evident and then later on I’ll come back and make corrections before this proof is finalized - so here goes….ready?

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I’m pretty sure I may have missed one or there may be a redundant one, but guess what? If that is the case - tis no big deal - I’ll come back and correct it when I figure out myself or somebody chimes in with a little bit of help - I could use all the help I can get.

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edit - this is a quick post here and probably full of error, but guess what - I don’t care

Holy - Moly….somebody is gonna need to do some editing on this I think!

Hey - here is some music - dire straits….

I’m gonna check this all out fore it goes final - you know don’t ya?

the time now - tis 12423 230

Not kidding around.

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I might be half-way out of my mind already been time for the 10th shape diagnosis I reckon.

Maybe the 11th and 12th as well - cause once you figure the way to do it - then the cat is out of the bag!

What I’m gonna do is come in here - after the fact - make corrections but I’m working my way through these shapes that form from the 23 one made with five (5) hexagons each and after trial-and-error I’ll get to the final discrete shapes - beauty is - I already know there is a fixed number of them and the solution beckons - just like Odessa does!

BK

edit - I’m sticking this here now for the time being…

I should put a date on these comments - and in the hole time loses meaning, but the date just now is October 20, 2024 and the time is 9:46 pm or some such - you know per military time it could be expressed as such - 102024 2146 ….and here is another comment from the thread above saved for safe keeping on this article about hexagons and the number six I reckon.

BK - the answer I think is 88 - as shown in another article - I find it disappointing the number ain’t prime, but no matter - I had fun playing with the shapes harmless in imagination.