I've figured out Shapes #12 and #13 in my head. I'll try to at least pose those images fore the end of the day....."Shape #14" will reference back to a "new" shape when this was done for five (5) hexagons but the act of doing this puzzle the way I have has given me some ideas along the way and I think I will have a "speculative" answer - but then it will need to be double-checked!
Near the top of it there are four (4) shapes. 3a through 3d. These will be the "base shapes" for shapes #14 through #17 with six hexagons connected - is it not obvious the "six" would not even exist without "five", and moreover - is it not obvious than one thing connects to another and if you let the stream of thought flow fairly that better ideas are on the horizon?
Truly the beauty of working out a "harmless" geometry puzzle in so many different ways....the beauty is it helps find "errors" - nothing wrong with finding errors - they are part of life - an outcome of uncertainty no doubt, but nothing to be afraid of.
~
After awhile ones ability to find and correct errors improves rapidly - and if we are talking about the "human mind" versus some AI bot this kind of learning is awesome!
WOW - I stand in awe Ken - way over my pay-grade. But your link to the French Red Sea Op was well found on another thread - I can use this - thanks mate :-)
It is my humble opinion that Israel, the apartheid place it is - is bringing boycott upon itself and then it will no longer be under zionist influence - that is the hopeful outcome, but no doubt much suffering has already occurred - and for what?
Further, as I has speculated elsewhere, I suspect just like there are "drones in the air" - so be they in underwater.
I suspect most ships seeking passage are sitting ducks and this will become evident as the nation of Israel is boycotted in the seas, the air, the land, and most importantly of all - the mind.
They shall reap what they have sown.
And then - a baby will be born.
~
I want peace and I don't want any more babies to die -
I know I always don't get what I want and I know more babies in Gaza are likely starving and close to death....
Bert - sometimes "I fly" above my own maximum altitude I suppose. I've learned better how to land and more importantly I've learned better how NOT to waste energy lashing needlessly.
~
I've been thinking about these hexagons for a long time now - at its most base aspect, the purpose of this effort is to find "discrete" shapes independent of "orientation" 2-dimensionally with hexagon tiles connected. I've done this for shapes with 5 tiles and there are 23 total. Now, one-by-one I'm assessing the 23 shapes and determining "new" shapes (not redundant) that are created when a sixth tile is added.
~
So that is why in the images above (and in the previous article), I commence with a "base shape" out of the 23 total made from five (5) tiles, and then rotating around from a starting point, all new possible shapes are assessed when a 6th tile is added. If it is a shape not yet revealed - it is "new" per these criteria.
~
So, I've made it through 14 of the 23 shapes and the possibilities of "new" shapes are diminishing cause many of the fixed number of shapes have already been identified. I'm up to 73 shapes now (if I haven't made an error) - and I do need to double check these cause sometimes it can be challenging to recall what is already identified - but I think I'm about 3/4ths of the way through ALL the shapes with six hexagon tiles - and I KNOW there is a fixed discrete whole number correct answer for this puzzle! That is part of the beauty of it for me - plus the fact it is just harmless math and shape imagination!
It is just another way of thinking about things using "both sides" of our brain - I think while this may be harmless it does have value. I love in a way all this is best done without a calculator or a smart device and that even with all my thinking about it over the last few years I still make mistakes on my journey to "solve" this puzzle.
89 is prime, I'm biased, so I like that answer in a way - but seems that is the answer to this puzzle Bert.
Honestly, any AI worth its salt could be programmed to figure this out, but what you think the answer is? Just now I think it is 89 for goodness sake....but I haven't double-checked yet.
The main point of the puzzle is shape imagination two-dimensionally and there is no harm in it Bert - not a bit of harm in it. It is harmless.
I'm not harmless, but don't mean I can't contemplate harmless ideas.....some ideas however have proven themselves to be harmful - by now this ought be common understanding.
~
2024 is shaping up to be a year to remember - I think it is going to be better than '23 in many ways - the pendulum is turning back to balance and Lady Libra is waiting for it with the scales she holds with such firmness.
I will have to take your word on it. I am good at business math but that is about as far as it goes. I am hopeful next year will be better, and share in your optimism. I do admire your tenacity in figuring this out. My Wife is very tenacious at everything she does, so I am familiar with that personality type. Wishing you the best in the new year my friend.
Don't take my word for it - it can be verified - that is part of the beauty - I consider it "learning together".
I like learning with others.
Tenaciousness is going to be an important attribute for those of us with ideas for a better future - in 2024 I'm going to be more tenacious than I am now - I'm going to be more than determined, but I don't intend on being ruthless unless necessary - if necessary I will be.
Here I am now - tis 11:30 pm - the 11th hour - 2023 is coming to an end.
I'm going to maybe tomorrow look over this whole puzzle one set of images after another and following the logic I've discovered in this effort to solve the puzzle and bias set aside I will double-check the images and then I think I ought make a post shows the total solutions - I think the answer is 89 even if there may be mistakes in presentation, but maybe, just maybe the answer is out there and beckons and the puzzle has been solved?
Tis 11:32 now - the year coming to an end - I'm a proud citizen of NC and I stand proud with my brothers and sisters in love - together we are better - and know this - I stand with you directly - I stand strong in the strength of the hills and the river we reside within - I will defend to the end and my love is strong - tis indomitable.
Please put my love to the test - but know this - this puzzle - the solution beckons - the solution we all must know - if not given yet it will be - cause it is fixed, definitive and undeniable - so even if 89 ain't the answer - I think it is - the answer is known. It is known already - there is no uncertainty to it - that is the beauty of it - it is beauty undeniable.
~
2024 is going to be better - you can count on that - you can count on me to be there for you - I fight like a man on a mission of love - I fight - I play to win. I send my love out to all who desire and crave peace and harmony - in 2024 those who suffered are going to get recompense I think - in 2024 those forlorn will be lifted up and those who have harmed others will get justice. I can't wait - I'll be there for you - I hope you are there for me in vice-versa and together we are better is what I think.
~
Happy New Years everybody - tis but 21 minutes away - I await it with respect and honor for forces beyond and the power of love so strong that it blows fear away.
Tis 11:40 now....and now I go to be with the one I love.
Life is good and North Carolina is a state not to be trifled with....in NC we love it all....we got lots of love to share.
I had the free will to solve this puzzle - I know the puzzle may not be solved - I know there could be errors - I know all this, but I know I've displayed the methodology and I know that will outlive what I know I think maybe?
~
I think 89 is the answer, but I know that could be incorrect.
I know on 4824 a total eclipse is going to happen and I want you to be with me when it does.
I promise to be true to you - we know, we know, we know.....the baby been born.
So, OK, assuming the numbers are "correct" - the total is up to 81 now and I know there are more than two more - so "83" ain't the answer. I can prove it.
The number "89" might be, but my bet presently is on 91.
*
Place your bets!
Merry Christmas to all kind readers!
BK
**
my "backup" bet is on 97....the odds in my mind are presently as follows:
.......... #89 - 30%
........... #91 - 5%
............ #97 - 50%
............. something else - 15%.
~~~~
Place your bets on the 3 numbers above - no bets allowed on "something else"!
OK - speculative answer for the puzzle - 89.
89 is a prime number and I may be biased.
Work will be double-checked.
BK
I've figured out Shapes #12 and #13 in my head. I'll try to at least pose those images fore the end of the day....."Shape #14" will reference back to a "new" shape when this was done for five (5) hexagons but the act of doing this puzzle the way I have has given me some ideas along the way and I think I will have a "speculative" answer - but then it will need to be double-checked!
~
Peace on Earth!
BK
122323 1313
Hey - I'm posting this for my own sake. What I need to do next is go back to this article here:
https://buffaloken.substack.com/p/a-proof
Near the top of it there are four (4) shapes. 3a through 3d. These will be the "base shapes" for shapes #14 through #17 with six hexagons connected - is it not obvious the "six" would not even exist without "five", and moreover - is it not obvious than one thing connects to another and if you let the stream of thought flow fairly that better ideas are on the horizon?
Truly the beauty of working out a "harmless" geometry puzzle in so many different ways....the beauty is it helps find "errors" - nothing wrong with finding errors - they are part of life - an outcome of uncertainty no doubt, but nothing to be afraid of.
~
After awhile ones ability to find and correct errors improves rapidly - and if we are talking about the "human mind" versus some AI bot this kind of learning is awesome!
Go Bills!
WOW - I stand in awe Ken - way over my pay-grade. But your link to the French Red Sea Op was well found on another thread - I can use this - thanks mate :-)
It is my humble opinion that Israel, the apartheid place it is - is bringing boycott upon itself and then it will no longer be under zionist influence - that is the hopeful outcome, but no doubt much suffering has already occurred - and for what?
Further, as I has speculated elsewhere, I suspect just like there are "drones in the air" - so be they in underwater.
I suspect most ships seeking passage are sitting ducks and this will become evident as the nation of Israel is boycotted in the seas, the air, the land, and most importantly of all - the mind.
They shall reap what they have sown.
And then - a baby will be born.
~
I want peace and I don't want any more babies to die -
I know I always don't get what I want and I know more babies in Gaza are likely starving and close to death....
~
They shall reap what they have sown.
~
JUSTIFIED RETRIBUTION
is on the way....
With you Ken - all the way.
You are flying above my maximum altitude on this one but I applaud and encourage you just the same.
Bert - sometimes "I fly" above my own maximum altitude I suppose. I've learned better how to land and more importantly I've learned better how NOT to waste energy lashing needlessly.
~
I've been thinking about these hexagons for a long time now - at its most base aspect, the purpose of this effort is to find "discrete" shapes independent of "orientation" 2-dimensionally with hexagon tiles connected. I've done this for shapes with 5 tiles and there are 23 total. Now, one-by-one I'm assessing the 23 shapes and determining "new" shapes (not redundant) that are created when a sixth tile is added.
~
So that is why in the images above (and in the previous article), I commence with a "base shape" out of the 23 total made from five (5) tiles, and then rotating around from a starting point, all new possible shapes are assessed when a 6th tile is added. If it is a shape not yet revealed - it is "new" per these criteria.
~
So, I've made it through 14 of the 23 shapes and the possibilities of "new" shapes are diminishing cause many of the fixed number of shapes have already been identified. I'm up to 73 shapes now (if I haven't made an error) - and I do need to double check these cause sometimes it can be challenging to recall what is already identified - but I think I'm about 3/4ths of the way through ALL the shapes with six hexagon tiles - and I KNOW there is a fixed discrete whole number correct answer for this puzzle! That is part of the beauty of it for me - plus the fact it is just harmless math and shape imagination!
It is just another way of thinking about things using "both sides" of our brain - I think while this may be harmless it does have value. I love in a way all this is best done without a calculator or a smart device and that even with all my thinking about it over the last few years I still make mistakes on my journey to "solve" this puzzle.
~
Warm Regards,
Ken
You certainly have much mental energy, I admire that. Merry Christmas.
Seems the answer may be 89.
89 is prime, I'm biased, so I like that answer in a way - but seems that is the answer to this puzzle Bert.
Honestly, any AI worth its salt could be programmed to figure this out, but what you think the answer is? Just now I think it is 89 for goodness sake....but I haven't double-checked yet.
The main point of the puzzle is shape imagination two-dimensionally and there is no harm in it Bert - not a bit of harm in it. It is harmless.
I'm not harmless, but don't mean I can't contemplate harmless ideas.....some ideas however have proven themselves to be harmful - by now this ought be common understanding.
~
2024 is shaping up to be a year to remember - I think it is going to be better than '23 in many ways - the pendulum is turning back to balance and Lady Libra is waiting for it with the scales she holds with such firmness.
~
Ken
I will have to take your word on it. I am good at business math but that is about as far as it goes. I am hopeful next year will be better, and share in your optimism. I do admire your tenacity in figuring this out. My Wife is very tenacious at everything she does, so I am familiar with that personality type. Wishing you the best in the new year my friend.
Don't take my word for it - it can be verified - that is part of the beauty - I consider it "learning together".
I like learning with others.
Tenaciousness is going to be an important attribute for those of us with ideas for a better future - in 2024 I'm going to be more tenacious than I am now - I'm going to be more than determined, but I don't intend on being ruthless unless necessary - if necessary I will be.
We think along the same lines on this.
Here I am now - tis 11:30 pm - the 11th hour - 2023 is coming to an end.
I'm going to maybe tomorrow look over this whole puzzle one set of images after another and following the logic I've discovered in this effort to solve the puzzle and bias set aside I will double-check the images and then I think I ought make a post shows the total solutions - I think the answer is 89 even if there may be mistakes in presentation, but maybe, just maybe the answer is out there and beckons and the puzzle has been solved?
Tis 11:32 now - the year coming to an end - I'm a proud citizen of NC and I stand proud with my brothers and sisters in love - together we are better - and know this - I stand with you directly - I stand strong in the strength of the hills and the river we reside within - I will defend to the end and my love is strong - tis indomitable.
Please put my love to the test - but know this - this puzzle - the solution beckons - the solution we all must know - if not given yet it will be - cause it is fixed, definitive and undeniable - so even if 89 ain't the answer - I think it is - the answer is known. It is known already - there is no uncertainty to it - that is the beauty of it - it is beauty undeniable.
~
2024 is going to be better - you can count on that - you can count on me to be there for you - I fight like a man on a mission of love - I fight - I play to win. I send my love out to all who desire and crave peace and harmony - in 2024 those who suffered are going to get recompense I think - in 2024 those forlorn will be lifted up and those who have harmed others will get justice. I can't wait - I'll be there for you - I hope you are there for me in vice-versa and together we are better is what I think.
~
Happy New Years everybody - tis but 21 minutes away - I await it with respect and honor for forces beyond and the power of love so strong that it blows fear away.
Tis 11:40 now....and now I go to be with the one I love.
Life is good and North Carolina is a state not to be trifled with....in NC we love it all....we got lots of love to share.
I had the free will to solve this puzzle - I know the puzzle may not be solved - I know there could be errors - I know all this, but I know I've displayed the methodology and I know that will outlive what I know I think maybe?
~
I think 89 is the answer, but I know that could be incorrect.
I know on 4824 a total eclipse is going to happen and I want you to be with me when it does.
I promise to be true to you - we know, we know, we know.....the baby been born.
~
2024 - just the start of better times beginning!
I think I've about got this puzzle figured out!
I think I sort already know the answer.....
I'm just not sure I want to find it....
but I will!
~
BK
So, OK, assuming the numbers are "correct" - the total is up to 81 now and I know there are more than two more - so "83" ain't the answer. I can prove it.
The number "89" might be, but my bet presently is on 91.
*
Place your bets!
Merry Christmas to all kind readers!
BK
**
my "backup" bet is on 97....the odds in my mind are presently as follows:
.......... #89 - 30%
........... #91 - 5%
............ #97 - 50%
............. something else - 15%.
~~~~
Place your bets on the 3 numbers above - no bets allowed on "something else"!
~
Merry Christmas!
Ken
That was a fool's bet.
Payout for 89 forthecoming -
after I double-check of course...
How bout those Buffalo Bills? They "pulled it off" in the end - won the game 24-22. That was fun.
Now - I got a puzzle to solve fore the end of '23.