Rainbow Lego Blocks and Pattern Combinations

[tuckerkao]

What is the purpose of the lego digital designer program?
Does it tie to 3d printing?

This Lego software can also generate the building guide which makes any logical models possible to build. I have the free version currently.

The professional version can link to the 3D printing, need more programs and plug-ins which I haven't figure it out yet.

It's also nice that there are online stores where people can buy individual Lego parts.

 

[Kyriakos]

This Lego software can also generate the building guide which makes any logical models possible to build. I have the free version currently.

The professional version can link to the 3D printing, need more programs and plug-ins which I haven't figure it out yet.

It's also nice that there are online stores where people can buy individual Lego parts.

I was basically asking if one can make money out of the (free) version

 

[tuckerkao]

I was basically asking if one can make money out of the (free) version

I don't think you can make money without having to buy the base set of required software and real Lego parts. There are also some models which must be built in real life since the weight supporting calculations may not always be correct in the digital software all the time.

The building guide can be freely generated into the html pages, dozenal math shouldn't be the problem, just follow the individual instructions step by step.

 

[Kyriakos]

No money no interest :/

 

[tuckerkao]

No money no interest :/

Here's a video of 3D Printing for Lego Bricks -

It's like an advanced copy machine, you'll need an original document to copy and paste on to the new blank page.

In order to 3D print a new brick, there has to be an original brick available -

 

[tuckerkao]

May be thousands of fans are already writing angry letters to him, complaining that these lego columns are too complex.

Lego math game takes 1 minute to learn, life time to master. The easiest levels are for the preschool kids.
https://www.notimeforflashcards.com/2014/07/lego-math-game-for-preschool-2.html

I always enjoy to practice King-Bishop-Knight checkmate on the chess board. It's ultra hard for people who only use the decimal base, The movements of the knight tie directly to the patterns of the dozenal math and can be explained using type of lego towers I've posted. In the real world, millions of people have complained that Chess is too hard for them.

In very many times, people were unhappy about me because my knight took their queen out of the board due to some dozenal math behind the scene.

 

[Kyriakos]

Well, you could make something which people into chess would be lured to care more about, as an oddity. For example iirc there are only 12 unique (not based on some type of set of symmetricals) solutions of how to place 8 queens on a chessboard without any one attacking the others.
Even counting all possibilities, they are less than 100 (iirc 92 or similar).

See, if you really want to place the next piece in your lego set, you first have to place those 8 queens correctly. Otherwise just stick to regular school, you aren't gifted

 

[tuckerkao]

Well, you could make something which people into chess would be lured to care more about, as an oddity. For example iirc there are only 12 unique (not based on some type of set of symmetricals) solutions of how to place 8 queens on a chessboard without any one attacking the others.
Even counting all possibilities, they are less than 100 (iirc 92 or similar).

See, if you really want to place the next piece in your lego set, you first have to place those 8 queens correctly. Otherwise just stick to regular school, you aren't gifted

The easiest solution will be placing the queens in several sets of the knight jumps since queen = rook + bishop.

 

[Kyriakos]

The easiest solution will be placing the queens in several sets of the knight jumps since queen = rook + bishop. (2, 4, 6, 8), (1, 3), (5, 7) which go from row 1 to row 8.

When I first heard of the question I was going to find the common set of the rook,bishop safe positions. However the calculations needed are still very considerable if you set out to do this.
I also had thought of using trigonometry in a dot matrix. Again will take a lot of time.

I actually did try to place the queens with calculation-on-the-go, ie noticing which new positions had the least conflicts (which is a strategy, but you do need to start with a few first spots that are part of one of the possible 90+) and got to being able to place 7 queens.

Here is one of the possible solutions:

(from https://en.wikipedia.org/wiki/Eight_queens_puzzle, which has an article on the issue)

Not being a chess enthusiast, I do not know the correlation between the knight's moves and the combination of rook and bishop, so cannot say anything about your idea's foundation. Although intuitively one can tell that a queen being 2,1 away from another is economical (and works as you can see in the chosen example as well, but I think this example is the only one where all queens have a knight-move distance from at least one other)

 

[tuckerkao]

This solution consists a 4 knight jumping sequence and 2 more 2 knight jumps -

 

[Kyriakos]

Ok, I should have never got into commenting about knights

 

[red_elk]

I always enjoy to practice King-Bishop-Knight checkmate on the chess board. It's ultra hard for people who only use the decimal base

It's not ultra-hard actually, neither it requires usage of decimal/dozenal bases. Most players don't bother to learn it because this ending occurs extremely rare in practical games.

 

[tuckerkao]

Ok, I should have never got into commenting about knights

I just figured out another 8 queens solution with the knight jumps.

It's not ultra-hard actually, neither it requires usage of decimal/dozenal bases. Most players don't bother to learn it because this ending occurs extremely rare in practical games.

The knight jump patterns can be observed from the dozenal 5 multiplication table or other divisions of 5 methods -

Spoiler Knight Jump Patterns in x5 :

 

[Kyriakos]

@tuckerkao , you are a chess enthusiast, can you provide a brief proof of why the knight can reach (given enough moves) every square on the 8x8 board?
I'd appreciate it even more if the proof explicitly uses the circle, but you can do it in any way you feel like it.

 

[tuckerkao]

@tuckerkao , you are a chess enthusiast, can you provide a brief proof of why the knight can reach (given enough moves) every square on the 8x8 board?
I'd appreciate it even more if the proof explicitly uses the circle, but you can do it in any way you feel like it.

The smallest possible dimension to perform the knight tour to every square is on the 4x3 board which explains why the dozenal math formula directly link to this specific chess piece -

Red ball to Purple ball, then Red stone to Purple stone.

 

[Kyriakos]

The smallest possible dimension to perform the knight tour to every square is on the 4x3 board which explains why the dozenal math formula directly link to this specific chess piece -

View attachment 570255

Red ball to Purple ball, then Red stone to Purple stone.

Hey, that is too cryptic (it wouldn't be a proof in the typical sense even if I had asked for the 4x3 board)
In other words, I am not looking for a list of the moves which make all squares accessible, but a few lines of proof as to why this is the case.
I can easily suppose the 4x3 is part of the proof, due to 12, but can't follow the proof by that alone.

 

[tuckerkao]

Hey, that is too cryptic (it wouldn't be a proof in the typical sense even if I had asked for the 4x3 board)
In other words, I am not looking for a list of the moves which make all squares accessible, but a few lines of proof as to why this is the case.
I can easily suppose the 4x3 is part of the proof, due to 12, but can't follow the proof by that alone.

This is the type of knight tour game which you win by landing on each square only once. The boards don't have to be square to rectangle, can be any logical shapes that have at least 1 solution.

Spoiler Knight Tour to Every Square Enhanced :

 

[Kyriakos]

Ok, it isn't the format of proof I am looking for, but thanks anyway (it's not like this is the topic of the thread in the first place ^_^ )

 

[tuckerkao]

Ok, it isn't the format of proof I am looking for, but thanks anyway (it's not like this is the topic of the thread in the first place ^_^ )

Here's the solution for the standard 8x8 chess board -

Any arrays of the color balls and stones can be built as the Lego Towers as long as they are not too gigantic in dimensions. The knight jump is a type of pattern combination that can be integrated into many toy playing strategies and problem solving functions while creating interesting graphic effects. Some people like them when they have no ideas that the dozenal math is hidden behind the scene.

The Lego Tower looks better with 2 pairs of the above patterns stack upon each other -

Spoiler Knight Tour Lego Towers on the Ramp :

 

[Kyriakos]

I am not doubting this is a proof, it just isn't the form I asked for.
I am sure you get this, just to give a very simple illustration of something very similar:

Let's say I told you that 0<a<1, and I wanted you to prove that a^3<a

You could always just say: "well, it is pretty obvious that any number which is smaller than 1, will become even smaller when multiplied with itself, so even smaller when multiplied twice with itself". Which would be obviously true.
But it wouldn't be as formal a proof as if you wrote the following:

which is always true since a>0, (a-1)<0 and (a+1)>0, thus you have positiveXnegativeXpositive<0

Likewise, I do not doubt you can place the knight on all positions. I was hoping for a proof starting with the circle the knight covers (here the center of the circle is cyan, the perimetric spots are green, red is the next move, yellow the next).

I could use a formal proof going by the circle and expansions of it in the grid, but I will have to construct it myself, I am not greedy ^_^