On July 13, Mike Terry wrote:
> >>>>>>>>> Each block has one face painted with A, as shown.
> >>>>>>>>> A block moves as follows: it moves into an empty
> >>>>>>>>> adjacent cell. It rolls over an edge, accomplishing a 1/4 turn.
>
> >>>>>>> Sorry for the stupid question, buts its 3d where if I move a block with
> >>>>>>> an A on it to the right the the A face will be rotated 1/4 turn so that
> >>>>>>> the A is on the right hand side of the block, no longer facing me?
>
> >>>>>> Correct.
> >>>>>> It's a 3-D context. End with 5 in a row. No tricks.
>
>>> The A would be on top again, but upside down, i.e. not "in the same original orientation". I.e.
>>> it would end up:
>>> _________________________
> >> |___|___|___|___|___|___|
> >> |___|___|___|___|___|___|
> >> |___|___|___|___|___|___|
> >> |___|___|_∀_|___|___|___|
> >> |___|___|___|___|___|___|
> >> |___|___|___|___|___|___|
>
>> We need to get clarification if a solution just needs all A's up, their rotations be dammed... Or if
>> they all must be A, not some upside down A, or a right or left A. Humm....
>
>>> If so, that would severely limit possible solutions, as a given starting block would be forced to
>>> move an even number of cells (horizontal+vertical moves) for the final solution - meaning it could
>>> only end up on squares of its own colour if we were using a chess board..
> >> In fact, if that's how things are there would be no solution, as the starting position has 4 black
>>> and 1 white square, but we are asked to end up with a 3-2 split of black/white, which would be
>>> impossible.
>
> I thought about it in bed before I finally dropped off, and decided there was indeed such a parity
> constraint, assuming the As must all end up the right way up, not rotated or upside down. So the
> problem has no solution.

Parity is the key idea. A block can perform an even or odd number of moves,
what are the implications of each? Consider that the blocks cover 4 black cells
to start, then end on 2 or 3 blacks.

Any good puzzle is "aha" -

> Here's a quick outline of a proof:
> 1) first just think of a cube with no A, but marked with what I'll call "parity lines":
> Labelling the faces T,B,N,E,S,W (for top, bottom, north, east, south and west).
> Bisect the faces T,B with a north/south line.
> Bisect the faces N,S with a horizontal (east/west) line.
> Bisect the faces E,W with a vertical line.
> 2) So each face has a bisecting line, and if we roll the cube around on a grid, as in
> the OP's problem, there are just two distinguished orientations for the cube:
> - all the parity lines match up with the lines in the starting position.
> Call this "even parity".
> - all the parity lines are perpendicular to the lines in the starting position.
> Call this "odd parity".
> 3) Key observation: every individual "roll" of the cube about one of its
> edges rotates it by 90 degrees, AND FLIPS THE PARITY between even/odd parity.
> 4) If the cube is rolled along a path through the grid, the parity of the cube
> is fully determined by whether an even/odd number of rolls has been performed.
> So if the cube starts with even parity on a black chess-board square, it will
> be even parity when it gets to any black square, and odd parity on any white
> square.
> 5) Now marking the A on one face, as in Rich's problem... Obviously the A stays
> alligned with its parity line as the cube rolls along a path.
> 6) So if we require the final A to be "the right way up" as we view it, the
> cube must end up with the even parity orientation (which it started with)
> otherwise if the final parity were odd the A would be showing
> sideways (along with it's associated parity line).
> 7) As noted in (4) the even parity positions are the squares of the same colour
> as the cube's starting square.
> 8) Er, that's it!

Not quite my idea of quick -

--
Rich

On 7/13/2023 12:13 PM, RichD wrote:
> On July 13, Mike Terry wrote:
>>>>>>>>>>> Each block has one face painted with A, as shown.
>>>>>>>>>>> A block moves as follows: it moves into an empty
>>>>>>>>>>> adjacent cell. It rolls over an edge, accomplishing a 1/4 turn.
>>
>>>>>>>>> Sorry for the stupid question, buts its 3d where if I move a block with
>>>>>>>>> an A on it to the right the the A face will be rotated 1/4 turn so that
>>>>>>>>> the A is on the right hand side of the block, no longer facing me?
>>
>>>>>>>> Correct.
>>>>>>>> It's a 3-D context. End with 5 in a row. No tricks.
>>
>>>> The A would be on top again, but upside down, i.e. not "in the same original orientation". I.e.
>>>> it would end up:
>>>> _________________________
>>>> |___|___|___|___|___|___|
>>>> |___|___|___|___|___|___|
>>>> |___|___|___|___|___|___|
>>>> |___|___|_∀_|___|___|___|
>>>> |___|___|___|___|___|___|
>>>> |___|___|___|___|___|___|
>>
>>> We need to get clarification if a solution just needs all A's up, their rotations be dammed... Or if
>>> they all must be A, not some upside down A, or a right or left A. Humm...
>>
>>>> If so, that would severely limit possible solutions, as a given starting block would be forced to
>>>> move an even number of cells (horizontal+vertical moves) for the final solution - meaning it could
>>>> only end up on squares of its own colour if we were using a chess board.
>>>> In fact, if that's how things are there would be no solution, as the starting position has 4 black
>>>> and 1 white square, but we are asked to end up with a 3-2 split of black/white, which would be
>>>> impossible.
>>
>> I thought about it in bed before I finally dropped off, and decided there was indeed such a parity
>> constraint, assuming the As must all end up the right way up, not rotated or upside down. So the
>> problem has no solution.
>
> Parity is the key idea. A block can perform an even or odd number of moves,
> what are the implications of each? Consider that the blocks cover 4 black cells
> to start, then end on 2 or 3 blacks.
>
> Any good puzzle is "aha" -
>
>> Here's a quick outline of a proof:
>> 1) first just think of a cube with no A, but marked with what I'll call "parity lines":
>> Labelling the faces T,B,N,E,S,W (for top, bottom, north, east, south and west).
>> Bisect the faces T,B with a north/south line.
>> Bisect the faces N,S with a horizontal (east/west) line.
>> Bisect the faces E,W with a vertical line.
>> 2) So each face has a bisecting line, and if we roll the cube around on a grid, as in
>> the OP's problem, there are just two distinguished orientations for the cube:
>> - all the parity lines match up with the lines in the starting position.
>> Call this "even parity".
>> - all the parity lines are perpendicular to the lines in the starting position.
>> Call this "odd parity".
>> 3) Key observation: every individual "roll" of the cube about one of its
>> edges rotates it by 90 degrees, AND FLIPS THE PARITY between even/odd parity.
>> 4) If the cube is rolled along a path through the grid, the parity of the cube
>> is fully determined by whether an even/odd number of rolls has been performed.
>> So if the cube starts with even parity on a black chess-board square, it will
>> be even parity when it gets to any black square, and odd parity on any white
>> square.
>> 5) Now marking the A on one face, as in Rich's problem... Obviously the A stays
>> alligned with its parity line as the cube rolls along a path.
>> 6) So if we require the final A to be "the right way up" as we view it, the
>> cube must end up with the even parity orientation (which it started with)
>> otherwise if the final parity were odd the A would be showing
>> sideways (along with it's associated parity line).
>> 7) As noted in (4) the even parity positions are the squares of the same colour
>> as the cube's starting square.
>> 8) Er, that's it!
>
> Not quite my idea of quick -

For some damn reason I am thinking of instant insanity:

https://www.etsy.com/listing/1313411691/vintage-1986-instant-insanity-cube

;^)

On Thursday, July 13, 2023 at 7:37:48 PM UTC-4, Chris M. Thomasson wrote:
> On 7/13/2023 12:13 PM, RichD wrote:
> > On July 13, Mike Terry wrote:
> >>>>>>>>>>> Each block has one face painted with A, as shown.
> >>>>>>>>>>> A block moves as follows: it moves into an empty
> >>>>>>>>>>> adjacent cell. It rolls over an edge, accomplishing a 1/4 turn.
> >>
> >>>>>>>>> Sorry for the stupid question, buts its 3d where if I move a block with
> >>>>>>>>> an A on it to the right the the A face will be rotated 1/4 turn so that
> >>>>>>>>> the A is on the right hand side of the block, no longer facing me?
> >>
> >>>>>>>> Correct.
> >>>>>>>> It's a 3-D context. End with 5 in a row. No tricks.
> >>
> >>>> The A would be on top again, but upside down, i.e. not "in the same original orientation". I.e.
> >>>> it would end up:
> >>>> _________________________
> >>>> |___|___|___|___|___|___|
> >>>> |___|___|___|___|___|___|
> >>>> |___|___|___|___|___|___|
> >>>> |___|___|_∀_|___|___|___|
> >>>> |___|___|___|___|___|___|
> >>>> |___|___|___|___|___|___|
> >>
> >>> We need to get clarification if a solution just needs all A's up, their rotations be dammed... Or if
> >>> they all must be A, not some upside down A, or a right or left A. Humm...
> >>
> >>>> If so, that would severely limit possible solutions, as a given starting block would be forced to
> >>>> move an even number of cells (horizontal+vertical moves) for the final solution - meaning it could
> >>>> only end up on squares of its own colour if we were using a chess board.
> >>>> In fact, if that's how things are there would be no solution, as the starting position has 4 black
> >>>> and 1 white square, but we are asked to end up with a 3-2 split of black/white, which would be
> >>>> impossible.
> >>
> >> I thought about it in bed before I finally dropped off, and decided there was indeed such a parity
> >> constraint, assuming the As must all end up the right way up, not rotated or upside down. So the
> >> problem has no solution.
> >
> > Parity is the key idea. A block can perform an even or odd number of moves,
> > what are the implications of each? Consider that the blocks cover 4 black cells
> > to start, then end on 2 or 3 blacks.
> >
> > Any good puzzle is "aha" -
> >
> >> Here's a quick outline of a proof:
> >> 1) first just think of a cube with no A, but marked with what I'll call "parity lines":
> >> Labelling the faces T,B,N,E,S,W (for top, bottom, north, east, south and west).
> >> Bisect the faces T,B with a north/south line.
> >> Bisect the faces N,S with a horizontal (east/west) line.
> >> Bisect the faces E,W with a vertical line.
> >> 2) So each face has a bisecting line, and if we roll the cube around on a grid, as in
> >> the OP's problem, there are just two distinguished orientations for the cube:
> >> - all the parity lines match up with the lines in the starting position.
> >> Call this "even parity".
> >> - all the parity lines are perpendicular to the lines in the starting position.
> >> Call this "odd parity".
> >> 3) Key observation: every individual "roll" of the cube about one of its
> >> edges rotates it by 90 degrees, AND FLIPS THE PARITY between even/odd parity.
> >> 4) If the cube is rolled along a path through the grid, the parity of the cube
> >> is fully determined by whether an even/odd number of rolls has been performed.
> >> So if the cube starts with even parity on a black chess-board square, it will
> >> be even parity when it gets to any black square, and odd parity on any white
> >> square.
> >> 5) Now marking the A on one face, as in Rich's problem... Obviously the A stays
> >> alligned with its parity line as the cube rolls along a path.
> >> 6) So if we require the final A to be "the right way up" as we view it, the
> >> cube must end up with the even parity orientation (which it started with)
> >> otherwise if the final parity were odd the A would be showing
> >> sideways (along with it's associated parity line).
> >> 7) As noted in (4) the even parity positions are the squares of the same colour
> >> as the cube's starting square.
> >> 8) Er, that's it!
> >
> > Not quite my idea of quick -
> For some damn reason I am thinking of instant insanity:
>
> https://www.etsy.com/listing/1313411691/vintage-1986-instant-insanity-cube
>
> ;^)

Rich,
I got as far as -- bottom row 234 (trivial) 234--5. (--) spot for1. All four with correct orientation of A.
[__]_1]__ ]
[_2]_3]_4] My starting layout.
[__]_5]__]
But moving (1) to get the right orientation is impossible.
The map looks like this---

O1OXOX
XOXOXO <--- the second 0 to the left is why this puzzle is impossible.
OXXXOX
XXXOXO
XXOXOX
23.4--5X <---(--) is the space for(1)
The (1) is on an X and position (--)is a spot for (1) and that position is also a 0.
In other words starting on an X you will never land on a 0 for the orientation of A .
Twist and turns or straight runs all you want but it isn't going to happen.
Strange how it lets you get this far and blocks you on the 0 squares trying to
place (1).

Dan

On Friday, July 14, 2023 at 12:30:00 AM UTC-4, Dan joyce wrote:
> On Thursday, July 13, 2023 at 7:37:48 PM UTC-4, Chris M. Thomasson wrote:
> > On 7/13/2023 12:13 PM, RichD wrote:
> > > On July 13, Mike Terry wrote:
> > >>>>>>>>>>> Each block has one face painted with A, as shown.
> > >>>>>>>>>>> A block moves as follows: it moves into an empty
> > >>>>>>>>>>> adjacent cell. It rolls over an edge, accomplishing a 1/4 turn.
> > >>
> > >>>>>>>>> Sorry for the stupid question, buts its 3d where if I move a block with
> > >>>>>>>>> an A on it to the right the the A face will be rotated 1/4 turn so that
> > >>>>>>>>> the A is on the right hand side of the block, no longer facing me?
> > >>
> > >>>>>>>> Correct.
> > >>>>>>>> It's a 3-D context. End with 5 in a row. No tricks.
> > >>
> > >>>> The A would be on top again, but upside down, i.e. not "in the same original orientation". I.e.
> > >>>> it would end up:
> > >>>> _________________________
> > >>>> |___|___|___|___|___|___|
> > >>>> |___|___|___|___|___|___|
> > >>>> |___|___|___|___|___|___|
> > >>>> |___|___|_∀_|___|___|___|
> > >>>> |___|___|___|___|___|___|
> > >>>> |___|___|___|___|___|___|
> > >>
> > >>> We need to get clarification if a solution just needs all A's up, their rotations be dammed... Or if
> > >>> they all must be A, not some upside down A, or a right or left A. Humm...
> > >>
> > >>>> If so, that would severely limit possible solutions, as a given starting block would be forced to
> > >>>> move an even number of cells (horizontal+vertical moves) for the final solution - meaning it could
> > >>>> only end up on squares of its own colour if we were using a chess board.
> > >>>> In fact, if that's how things are there would be no solution, as the starting position has 4 black
> > >>>> and 1 white square, but we are asked to end up with a 3-2 split of black/white, which would be
> > >>>> impossible.
> > >>
> > >> I thought about it in bed before I finally dropped off, and decided there was indeed such a parity
> > >> constraint, assuming the As must all end up the right way up, not rotated or upside down. So the
> > >> problem has no solution.
> > >
> > > Parity is the key idea. A block can perform an even or odd number of moves,
> > > what are the implications of each? Consider that the blocks cover 4 black cells
> > > to start, then end on 2 or 3 blacks.
> > >
> > > Any good puzzle is "aha" -
> > >
> > >> Here's a quick outline of a proof:
> > >> 1) first just think of a cube with no A, but marked with what I'll call "parity lines":
> > >> Labelling the faces T,B,N,E,S,W (for top, bottom, north, east, south and west).
> > >> Bisect the faces T,B with a north/south line.
> > >> Bisect the faces N,S with a horizontal (east/west) line.
> > >> Bisect the faces E,W with a vertical line.
> > >> 2) So each face has a bisecting line, and if we roll the cube around on a grid, as in
> > >> the OP's problem, there are just two distinguished orientations for the cube:
> > >> - all the parity lines match up with the lines in the starting position.
> > >> Call this "even parity".
> > >> - all the parity lines are perpendicular to the lines in the starting position.
> > >> Call this "odd parity".
> > >> 3) Key observation: every individual "roll" of the cube about one of its
> > >> edges rotates it by 90 degrees, AND FLIPS THE PARITY between even/odd parity.
> > >> 4) If the cube is rolled along a path through the grid, the parity of the cube
> > >> is fully determined by whether an even/odd number of rolls has been performed.
> > >> So if the cube starts with even parity on a black chess-board square, it will
> > >> be even parity when it gets to any black square, and odd parity on any white
> > >> square.
> > >> 5) Now marking the A on one face, as in Rich's problem... Obviously the A stays
> > >> alligned with its parity line as the cube rolls along a path.
> > >> 6) So if we require the final A to be "the right way up" as we view it, the
> > >> cube must end up with the even parity orientation (which it started with)
> > >> otherwise if the final parity were odd the A would be showing
> > >> sideways (along with it's associated parity line).
> > >> 7) As noted in (4) the even parity positions are the squares of the same colour
> > >> as the cube's starting square.
> > >> 8) Er, that's it!
> > >
> > > Not quite my idea of quick -
> > For some damn reason I am thinking of instant insanity:
> >
> > https://www.etsy.com/listing/1313411691/vintage-1986-instant-insanity-cube
> >
> > ;^)
> Rich,
> I got as far as -- bottom row 234 (trivial) 234--5. (--) spot for1. All four with correct orientation of A.
> [__]_1]__ ]
> [_2]_3]_4] My starting layout.
> [__]_5]__]
> But moving (1) to get the right orientation is impossible.
> The map looks like this---
>
> O1OXOX
> XOXOXO <--- the second 0 to the left is why this puzzle is impossible.
> OXXXOX
> XXXOXO
> XXOXOX
> 23.4--5X <---(--) is the space for(1)
> The (1) is on an X and position (--)is a spot for (1) and that position is also a 0.
> In other words starting on an X you will never land on a 0 for the orientation of A .
> Twist and turns or straight runs all you want but it isn't going to happen.
> Strange how it lets you get this far and blocks you on the 0 squares trying to
> place (1).
>
> Dan
Here are the moves for (5)
Rotate 2,3,4 a full rotation to the bottom row. (trivial)
Now 1 and 5 remain.
Moving 5 onto many different squares the orientation of A starts.
This is why this is not an impossible puzzle. (I retract that statement)
Taking 5 from two---1/4 turns to the right which is already done.
and going up one 1/4 turn,
then to the left 1/4 turn,
then up 1/4 turn,
then right 1/4 turn,
then down 1/4 turn,
then left 1/4 turn,
this falls on the position where 4 once held and now A is orientated
but still not positioned for placement in the bottom row.
So continuing with 5 ---
down 1/4 turn,
right 1/4 turn,
down 1/4 turn,
right 1/4 turn,
up 1/4 turn,
left 1/4 turn,
up 1/2 turn, orientates A again. Two diagonals up and to the right
from 5's original position.
Still not positioned to line up on the bottom.
Continue from that position---
right 1/4 turn,
down 1/4 turn,
left 1/4 turn,
down a 1/4 turn,
right 1/4 turn,
and finally up 1/4 turn.
Now one full rotation down.
It is now positioned in the 5th spot on the bottom.

On 7/12/2023 1:34 PM, RichD wrote:
> Given a 6 x 6 checkerboard. At the top left, 5 blocks fill 5 squares,
> like so: (crappy ASCII graphics)
>
> ______________________
> |_A_|___|_A_|___|___|___|
> |___|_A_|___|___|___|___|
> |_A_|___|_A_|___|___|___|
> |___|___|____|___|___|___|
> |___|___|____|___|___|___|
> |___|___|____|___|___|___|
>
> Each block has one face painted with A, as shown.
> A block moves as follows: it moves into an empty
> adjacent cell. It rolls over an edge, accomplishing a 1/4 turn.
>
> Your mission, Hunter, should you decide to accept,
> is to align all blocks in a single row or column, with no
> intermittent spaces, such that each ends up in the same
> original orientation. Should you fail, your father the Supreme
> Warlord will, as usual, disavow any knowledge of your activities.
> Good luck, Hunter -
>

Funny, well, strange timing, humm. Anyway, I actually have to port my
cube mapped textures to my new engine. Well, it might be fun to visually
show your ascii graphics in 3d. Once that is done, I can easily show an
A on top and the rotations for some moves. Also, this might tie into
some work I am collaborating with Dan on. Humm...

On 7/13/2023 9:57 PM, Dan joyce wrote:
[...]

Finally got my older cube map code ported over:

https://i.ibb.co/R71KHyY/image.png

;^)

On Friday, July 14, 2023 at 3:51:36 AM UTC-4, Chris M. Thomasson wrote:
> On 7/13/2023 9:57 PM, Dan joyce wrote:
> [...]
>
> Finally got my older cube map code ported over:
>
> https://i.ibb.co/R71KHyY/image.png
>
> ;^)
RichD's profile photo
RichD
Jul 12, 2023, 5:23:35 PM (yesterday)
to
On July 12, RichD wrote:
> Given a 6 x 6 checkerboard. At the top left, 5 blocks fill 5 squares,
> like so: (crappy ASCII graphics)

of course I botched the diagram.
Re-try:
If the puzzle started like below, then the puzzle is easy to solve.
The top A moved one position to the right to start the puzzle.
No muss no fuss. ;=)
______________________
|___|_ _|_A_|___|___|___|
|_A_|_A_|_A_|___|___|___|
|___|_A_|____|___|___|___|
|___|___|____|___|___|___|
|___|___|____|___|___|___|
|___|___|____|___|___|___|

On Friday, July 14, 2023 at 10:12:06 AM UTC-4, Dan joyce wrote:
> On Friday, July 14, 2023 at 3:51:36 AM UTC-4, Chris M. Thomasson wrote:
> > On 7/13/2023 9:57 PM, Dan joyce wrote:
> > [...]
> >
> > Finally got my older cube map code ported over:
> >
> > https://i.ibb.co/R71KHyY/image.png
> >
> > ;^)
> RichD's profile photo
> RichD
> Jul 12, 2023, 5:23:35 PM (yesterday)
> to
> On July 12, RichD wrote:
> > Given a 6 x 6 checkerboard. At the top left, 5 blocks fill 5 squares,
> > like so: (crappy ASCII graphics)
> of course I botched the diagram.
> Re-try:
> If the puzzle started like below, then the puzzle is easy to solve.
> The top A moved one position to the right to start the puzzle.
> No muss no fuss. ;=)
> ______________________
> |___|_ _|_A_|___|___|___|
> |_A_|_A_|_A_|___|___|___|
> |___|_A_|____|___|___|___|
> |___|___|____|___|___|___|
> |___|___|____|___|___|___|
> |___|___|____|___|___|___|
Otherwise, impossible with the placement as presented and all
A's in line on the bottom.

On July 13, Dan joyce wrote:
> > > >>>>>>> Each block has one face painted with A, as shown.
> > > >>>>>>> A block moves as follows: it moves into an empty
> > > >>>>>>> adjacent cell. It rolls over an edge, accomplishing a 1/4 turn.
>
> > >> I thought about it in bed before I finally dropped off, and decided there was indeed such a parity
> > >> constraint, assuming the As must all end up the right way up, not rotated or upside down. So the
> > >> problem has no solution.
>
> > > > Parity is the key idea. A block can perform an even or odd number of moves,
> > > > what are the implications of each? Consider that the blocks cover 4 black cells
> > > > to start, then end on 2 or 3 blacks.
>
> This is why this is not an impossible puzzle. (I retract that statement)

One of the black square blocks must end on a white, hence an odd
number of moves. A block can regain its initial orientation only after
an even number of moves.

Still, pursuing the various attempts is a nice exercise in 3-D visualization,
a useful skill. Exercise is never a bad thing, whether the muscles of
the legs, or the one in the cranium -

--
Rich

On Friday, July 14, 2023 at 12:58:32 PM UTC-4, RichD wrote:
> On July 13, Dan joyce wrote:
> > > > >>>>>>> Each block has one face painted with A, as shown.
> > > > >>>>>>> A block moves as follows: it moves into an empty
> > > > >>>>>>> adjacent cell. It rolls over an edge, accomplishing a 1/4 turn.
> >
> > > >> I thought about it in bed before I finally dropped off, and decided there was indeed such a parity
> > > >> constraint, assuming the As must all end up the right way up, not rotated or upside down. So the
> > > >> problem has no solution.
> >
> > > > > Parity is the key idea. A block can perform an even or odd number of moves,
> > > > > what are the implications of each? Consider that the blocks cover 4 black cells
> > > > > to start, then end on 2 or 3 blacks.
> >
> > This is why this is not an impossible puzzle. (I retract that statement)
> One of the black square blocks must end on a white, hence an odd
> number of moves. A block can regain its initial orientation only after
> an even number of moves.
>
> Still, pursuing the various attempts is a nice exercise in 3-D visualization,
> a useful skill. Exercise is never a bad thing, whether the muscles of
> the legs, or the one in the cranium -
>
>
> --
> Rich
So Rich, you don't think this puzzle is impossible the way you presented it?

On 7/14/2023 7:12 AM, Dan joyce wrote:
> On Friday, July 14, 2023 at 3:51:36 AM UTC-4, Chris M. Thomasson wrote:
>> On 7/13/2023 9:57 PM, Dan joyce wrote:
>> [...]
>>
>> Finally got my older cube map code ported over:
>>
>> https://i.ibb.co/R71KHyY/image.png
>>
>> ;^)
> RichD's profile photo
> RichD
> Jul 12, 2023, 5:23:35 PM (yesterday)
> to
> On July 12, RichD wrote:
>> Given a 6 x 6 checkerboard. At the top left, 5 blocks fill 5 squares,
>> like so: (crappy ASCII graphics)
>
> of course I botched the diagram.
> Re-try:
> If the puzzle started like below, then the puzzle is easy to solve.
> The top A moved one position to the right to start the puzzle.
> No muss no fuss. ;=)
> ______________________
> |___|_ _|_A_|___|___|___|
> |_A_|_A_|_A_|___|___|___|
> |___|_A_|____|___|___|___|
> |___|___|____|___|___|___|
> |___|___|____|___|___|___|
> |___|___|____|___|___|___|

Inside a block:

https://i.ibb.co/mXVR7Ct/image.png

On 7/14/2023 7:12 AM, Dan joyce wrote:
> On Friday, July 14, 2023 at 3:51:36 AM UTC-4, Chris M. Thomasson wrote:
>> On 7/13/2023 9:57 PM, Dan joyce wrote:
>> [...]
>>
>> Finally got my older cube map code ported over:
>>
>> https://i.ibb.co/R71KHyY/image.png
>>
>> ;^)
> RichD's profile photo
> RichD
> Jul 12, 2023, 5:23:35 PM (yesterday)
> to
> On July 12, RichD wrote:
>> Given a 6 x 6 checkerboard. At the top left, 5 blocks fill 5 squares,
>> like so: (crappy ASCII graphics)
>
> of course I botched the diagram.
> Re-try:
> If the puzzle started like below, then the puzzle is easy to solve.
> The top A moved one position to the right to start the puzzle.
> No muss no fuss. ;=)
> ______________________
> |___|_ _|_A_|___|___|___|
> |_A_|_A_|_A_|___|___|___|
> |___|_A_|____|___|___|___|
> |___|___|____|___|___|___|
> |___|___|____|___|___|___|
> |___|___|____|___|___|___|

https://i.ibb.co/CJztBtv/image.png

;)

On 7/15/2023 1:15 PM, Chris M. Thomasson wrote:
> On 7/14/2023 7:12 AM, Dan joyce wrote:
>> On Friday, July 14, 2023 at 3:51:36 AM UTC-4, Chris M. Thomasson wrote:
>>> On 7/13/2023 9:57 PM, Dan joyce wrote:
>>> [...]
>>>
>>> Finally got my older cube map code ported over:
>>>
>>> https://i.ibb.co/R71KHyY/image.png
>>>
>>> ;^)
>> RichD's profile photo
>> RichD
>> Jul 12, 2023, 5:23:35 PM (yesterday)
>> to
>> On July 12, RichD wrote:
>>> Given a 6 x 6 checkerboard. At the top left, 5 blocks fill 5 squares,
>>> like so: (crappy ASCII graphics)
>>
>> of course I botched the diagram.
>> Re-try:
>> If the puzzle started like below, then the puzzle is easy to solve.
>> The top A moved one position to the right to start the puzzle.
>> No muss no fuss. ;=)
>> ______________________
>> |___|_   _|_A_|___|___|___|
>> |_A_|_A_|_A_|___|___|___|
>> |___|_A_|____|___|___|___|
>> |___|___|____|___|___|___|
>> |___|___|____|___|___|___|
>> |___|___|____|___|___|___|
>
>
> https://i.ibb.co/CJztBtv/image.png
>
> ;)

https://i.ibb.co/5hGR4c9/image.png

;^)

On 7/14/2023 7:43 AM, Dan joyce wrote:
> On Friday, July 14, 2023 at 10:12:06 AM UTC-4, Dan joyce wrote:
>> On Friday, July 14, 2023 at 3:51:36 AM UTC-4, Chris M. Thomasson wrote:
>>> On 7/13/2023 9:57 PM, Dan joyce wrote:
>>> [...]
>>>
>>> Finally got my older cube map code ported over:
>>>
>>> https://i.ibb.co/R71KHyY/image.png
>>>
>>> ;^)
>> RichD's profile photo
>> RichD
>> Jul 12, 2023, 5:23:35 PM (yesterday)
>> to
>> On July 12, RichD wrote:
>>> Given a 6 x 6 checkerboard. At the top left, 5 blocks fill 5 squares,
>>> like so: (crappy ASCII graphics)
>> of course I botched the diagram.
>> Re-try:
>> If the puzzle started like below, then the puzzle is easy to solve.
>> The top A moved one position to the right to start the puzzle.
>> No muss no fuss. ;=)
>> ______________________
>> |___|_ _|_A_|___|___|___|
>> |_A_|_A_|_A_|___|___|___|
>> |___|_A_|____|___|___|___|
>> |___|___|____|___|___|___|
>> |___|___|____|___|___|___|
>> |___|___|____|___|___|___|
> Otherwise, impossible with the placement as presented and all
> A's in line on the bottom.

https://i.ibb.co/CtwJ7X1/image.png

On Saturday, July 15, 2023 at 4:23:17 PM UTC-4, Chris M. Thomasson wrote:
> On 7/15/2023 1:15 PM, Chris M. Thomasson wrote:
> > On 7/14/2023 7:12 AM, Dan joyce wrote:
> >> On Friday, July 14, 2023 at 3:51:36 AM UTC-4, Chris M. Thomasson wrote:
> >>> On 7/13/2023 9:57 PM, Dan joyce wrote:
> >>> [...]
> >>>
> >>> Finally got my older cube map code ported over:
> >>>
> >>> https://i.ibb.co/R71KHyY/image.png
> >>>
> >>> ;^)
> >> RichD's profile photo
> >> RichD
> >> Jul 12, 2023, 5:23:35 PM (yesterday)
> >> to
> >> On July 12, RichD wrote:
> >>> Given a 6 x 6 checkerboard. At the top left, 5 blocks fill 5 squares,
> >>> like so: (crappy ASCII graphics)
> >>
> >> of course I botched the diagram.
> >> Re-try:
> >> If the puzzle started like below, then the puzzle is easy to solve.
> >> The top A moved one position to the right to start the puzzle.
> >> No muss no fuss. ;=)
> >> ______________________
> >> |___|_ _|_A_|___|___|___|
> >> |_A_|_A_|_A_|___|___|___|
> >> |___|_A_|____|___|___|___|
> >> |___|___|____|___|___|___|
> >> |___|___|____|___|___|___|
> >> |___|___|____|___|___|___|
> >
> >
> > https://i.ibb.co/CJztBtv/image.png
> >
> > ;)
> https://i.ibb.co/5hGR4c9/image.png
>
> ;^)
Now your cheating Chris. ;=)

On 7/15/2023 5:31 PM, Dan joyce wrote:
> On Saturday, July 15, 2023 at 4:23:17 PM UTC-4, Chris M. Thomasson wrote:
>> On 7/15/2023 1:15 PM, Chris M. Thomasson wrote:
>>> On 7/14/2023 7:12 AM, Dan joyce wrote:
>>>> On Friday, July 14, 2023 at 3:51:36 AM UTC-4, Chris M. Thomasson wrote:
>>>>> On 7/13/2023 9:57 PM, Dan joyce wrote:
>>>>> [...]
>>>>>
>>>>> Finally got my older cube map code ported over:
>>>>>
>>>>> https://i.ibb.co/R71KHyY/image.png
>>>>>
>>>>> ;^)
>>>> RichD's profile photo
>>>> RichD
>>>> Jul 12, 2023, 5:23:35 PM (yesterday)
>>>> to
>>>> On July 12, RichD wrote:
>>>>> Given a 6 x 6 checkerboard. At the top left, 5 blocks fill 5 squares,
>>>>> like so: (crappy ASCII graphics)
>>>>
>>>> of course I botched the diagram.
>>>> Re-try:
>>>> If the puzzle started like below, then the puzzle is easy to solve.
>>>> The top A moved one position to the right to start the puzzle.
>>>> No muss no fuss. ;=)
>>>> ______________________
>>>> |___|_ _|_A_|___|___|___|
>>>> |_A_|_A_|_A_|___|___|___|
>>>> |___|_A_|____|___|___|___|
>>>> |___|___|____|___|___|___|
>>>> |___|___|____|___|___|___|
>>>> |___|___|____|___|___|___|
>>>
>>>
>>> https://i.ibb.co/CJztBtv/image.png
>>>
>>> ;)
>> https://i.ibb.co/5hGR4c9/image.png
>>
>> ;^)
> Now your cheating Chris. ;=)

;^D The orientation of little Roxy's face? :^)

Btw, little Roxy, RIP! Little family Dog.

On Sunday, July 16, 2023 at 4:05:27 PM UTC-4, Chris M. Thomasson wrote:
> On 7/15/2023 5:31 PM, Dan joyce wrote:
> > On Saturday, July 15, 2023 at 4:23:17 PM UTC-4, Chris M. Thomasson wrote:
> >> On 7/15/2023 1:15 PM, Chris M. Thomasson wrote:
> >>> On 7/14/2023 7:12 AM, Dan joyce wrote:
> >>>> On Friday, July 14, 2023 at 3:51:36 AM UTC-4, Chris M. Thomasson wrote:
> >>>>> On 7/13/2023 9:57 PM, Dan joyce wrote:
> >>>>> [...]
> >>>>>
> >>>>> Finally got my older cube map code ported over:
> >>>>>
> >>>>> https://i.ibb.co/R71KHyY/image.png
> >>>>>
> >>>>> ;^)
> >>>> RichD's profile photo
> >>>> RichD
> >>>> Jul 12, 2023, 5:23:35 PM (yesterday)
> >>>> to
> >>>> On July 12, RichD wrote:
> >>>>> Given a 6 x 6 checkerboard. At the top left, 5 blocks fill 5 squares,
> >>>>> like so: (crappy ASCII graphics)
> >>>>
> >>>> of course I botched the diagram.
> >>>> Re-try:
> >>>> If the puzzle started like below, then the puzzle is easy to solve.
> >>>> The top A moved one position to the right to start the puzzle.
> >>>> No muss no fuss. ;=)
> >>>> ______________________
> >>>> |___|_ _|_A_|___|___|___|
> >>>> |_A_|_A_|_A_|___|___|___|
> >>>> |___|_A_|____|___|___|___|
> >>>> |___|___|____|___|___|___|
> >>>> |___|___|____|___|___|___|
> >>>> |___|___|____|___|___|___|
> >>>
> >>>
> >>> https://i.ibb.co/CJztBtv/image.png
> >>>
> >>> ;)
> >> https://i.ibb.co/5hGR4c9/image.png
> >>
> >> ;^)
> > Now your cheating Chris. ;=)
> ;^D The orientation of little Roxy's face? :^)
>
> Btw, little Roxy, RIP! Little family Dog.
They do become part of the family. You're right, Rocky could end up
in any possition.

On July 15, Chris M. Thomasson wrote:
> >>> Finally got my older cube map code ported over:
> >>>> https://i.ibb.co/R71KHyY/image.png
> https://i.ibb.co/CtwJ7X1/image.png

Nifty.
Those images are generated through a Java graphics library?

--
Rich

On 7/17/2023 12:45 PM, RichD wrote:
> On July 15, Chris M. Thomasson wrote:
>>>>> Finally got my older cube map code ported over:
>>>>>> https://i.ibb.co/R71KHyY/image.png
>> https://i.ibb.co/CtwJ7X1/image.png
>
> Nifty.
> Those images are generated through a Java graphics library?
[...]

OpenGL and C++. However, I can port it to javascript and webgl. Humm...

On 7/17/2023 6:21 AM, Dan joyce wrote:
> On Sunday, July 16, 2023 at 4:05:27 PM UTC-4, Chris M. Thomasson wrote:
>> On 7/15/2023 5:31 PM, Dan joyce wrote:
>>> On Saturday, July 15, 2023 at 4:23:17 PM UTC-4, Chris M. Thomasson wrote:
>>>> On 7/15/2023 1:15 PM, Chris M. Thomasson wrote:
>>>>> On 7/14/2023 7:12 AM, Dan joyce wrote:
>>>>>> On Friday, July 14, 2023 at 3:51:36 AM UTC-4, Chris M. Thomasson wrote:
>>>>>>> On 7/13/2023 9:57 PM, Dan joyce wrote:
[...]
>>> Now your cheating Chris. ;=)
>> ;^D The orientation of little Roxy's face? :^)
>>
>> Btw, little Roxy, RIP! Little family Dog.
> They do become part of the family. You're right, Rocky could end up
> in any possition.

Thanks, Dan! :^)

Fwiw, we actually called little Roxy, little Rocky Rue. As a sort of
slang. thanks Dan.

On 7/17/2023 12:45 PM, RichD wrote:
> On July 15, Chris M. Thomasson wrote:
>>>>> Finally got my older cube map code ported over:
>>>>>> https://i.ibb.co/R71KHyY/image.png
>> https://i.ibb.co/CtwJ7X1/image.png
>
> Nifty.
> Those images are generated through a Java graphics library?

Fwiw, here is some of my older webgl work, can you get t to run on your
end? Thanks:

http://fractallife247.com/test/webgl

?