 # Board coordinates

#1

I think we need a coordinates system, like in Chess, to name board positions. This way we should be able to talk about the board, setups and solutions. Any ideas?

The first question to solve: has TT board a 11×11 size?

#2

There are three common standards for labelling a hex-grid. One is to label the rows and the diagonals in one direction (so, for example: 1A, 1C, 2A, 2B, 2C, 2D, 3A, 3B, 3C, 3D, 3E, 4A, 4B, 4C, 4D, 4E, 4F, 5B, 5C, 5D, 5E, 5F, …, 10D, 10E, 10F, 10G, 10H, 10I, 11G). Another is to label the rows and each individual column (so 1D, 1H, 2C, 2E, 2G, 2I, 3B, 3D, 3F, 3H, 3J, 4A, 4C, 4E, 4G, 4I, 4K, 5B, 5D, 5F, 5H, 5J, …, 10A, 10C, 10E, 10G, 10I, 10K, 11F). The third is to give adjacent pairs of columns (or single zig-zag columns) the same label (so 1B, 1D, 2B, 2C, 2D, 2E, 3A, 3B, 3C, 3D, 3E, 4A, 4B, 4C, 4D, 4E, 4F, 5A, 5B, 5C, 5D, 5E, …, 10A, 10B, 10C, 10D, 10E, 10F, 11C)

Which is best depends on how it’s going to be used - each has its own advantages and disadvantages. The first means that a ball will either stay in the same letter or go up to the next letter each time it drops, but means that later rows start with higher letters. The second means the ball changes to an adjacent letter each time it drops a row, but rows alternately start with A and B, and horizontally adjacent locations don’t have adjacent letters. The third makes it easiest to tell which letter something is, since each row starts with A, but balls will sometimes stay the same letter, and sometimes go to an adjacent letter, with which is which depending on the row number.

For Turing Tumble, I’m inclined to suggest a labelling system based on the two diagonals, like so: 3A, 1C, 4A, 3B, 2C, 1D, 5A, 4B, 3C, 2D, 1E, 6A, 5B, 4C, 3D, 2E, 1F, 6B, 5C, 4D, 3E, 2F, … 9D, 8E, 7F, 6G, 5H, 4I, 7G - each time you drop to the left, the number increases by 1; dropping to the right increases the letter by 1. Of course, it does make reading numbers off the board a little trickier - the secret is that the number plus the letter is a constant for each row, though that constant is three more than the row number - and the middle of each row is either the one where number and letter are equal, or the two where they differ by one, depending on whether you’re looking at an odd or even row.

#3

Why not just use cartesian coordinates? With (0,0) being the bottom left peg working up to (8,9) for the top right peg. Row 8 would be missing (0,8) and (0,10) and row 9 missing (0,9),(1,9),(5,9),(9,9) and (10,9).

Or you could follow your chess analogy and use (a,1) to (k,10) ?

#4

Thanks a lot @rmsgrey! Your text, re-worded and mixed with board ASCII
representations, follows:

There are three common standards for labelling a hex-grid:

One is to label the rows and diagonals in one direction. The first means
that a ball will either stay in the same letter or go up to the next letter
each time it drops, but means that later rows start with higher letters.

Another is to label the rows and each individual column. The second means the
ball changes to an adjacent letter each time it drops a row, but rows

The third is to give adjacent pairs of columns (or single zig-zag columns) the
same label. The third makes it easiest to tell which letter something is,
since each row starts with A, but balls will sometimes stay the same letter,
and sometimes go to an adjacent letter, with which is which depending on the
row number.

``````        First                   Second                  Third

1   |  .A. .C.  |       1   |  .D. .H.  |       1   |  .B. .D.  |
2   | .A.B.C.D. |       2   | .C.E.G.I. |       2   | .B.C.D.E. |
3   |.A.B.C.D.E.|       3   |.B.D.F.H.J.|       3   |.A.B.C.D.E.|
4   |A.B.C.D.E.F|       4   |A.C.E.G.I.K|       4   |A.B.C.D.E.F|
5   |.B.C.D.E.F.|       5   |.B.D.F.H.J.|       5   |.A.B.C.D.E.|
6   |B.C.D.E.F.G|       6   |A.C.E.G.I.K|       6   |A.B.C.D.E.F|
7   |.C.D.E.F.G.|       7   |.B.D.F.H.J.|       7   |.A.B.C.D.E.|
8   |C.D.E.F.G.H|       8   |A.C.E.G.I.K|       8   |A.B.C.D.E.F|
9   |.D.E.F.G.H.|       9   |.B.D.F.H.J.|       9   |.A.B.C.D.E.|
10  |D.E.F.G.H.I|       10  |A.C.E.G.I.K|       10  |A.B.C.D.E.F|
11  |     G     |       11  |     F     |       11  |     C     |
``````

For Turing Tumble, I’m inclined to suggest a labelling system based on the two
diagonals, like so:

``````        3A, 1C,
4A, 3B, 2C, 1D,
5A, 4B, 3C, 2D, 1E,
6A, 5B, 4C, 3D, 2E, 1F,
6B, 5C, 4D, 3E, 2F,
...
9D, 8E, 7F, 6G, 5H, 4I,
7G,
``````

to the left, the number increases by 1; dropping to the right increases the
letter by 1. Of course, it does make reading numbers off the board a little
trickier – the secret is that the number plus the letter is a constant for each
row, though that constant is three more than the row number – and the middle of
each row is either the one where number and letter are equal, or the two where
they differ by one, depending on whether you’re looking at an odd or even row.

`````` N               R   K

3 |  .A. .C.  | 1   4
4 | .A.B.C.D. | 1   5
5 |.A.B.C.D.E.| 1   6
6 |A.B.C.D.E.F| 1   7
6 |.B.C.D.E.F.| 2   8
7 |B.C.D.E.F.G| 2   9
7 |.C.D.E.F.G.| 3  10
8 |C.D.E.F.G.H| 3  11
8 |.D.E.F.G.H.| 4  12
9 |D.E.F.G.H.I| 7  13
7 |     G     | 7  14
``````
• `N`: ???
• `R`: ???
• `K`: row constant (N + letter: A=1, B=2, &c.)
• Row number: `K - 3`

EDITED: the last board should be now correct. We need now better definitions for `N` and `R` (or more mnemonic letters).

#5

Yeah, that last board isn’t what I intended - the numbers should apply to the down-right diagonals, increasing as you move to the left - so the top-right diagonal CDEF should all be 1s. The N column gives the number for the left-most position, but the Ks should be 1,1,1,1,2,2,3,3,4,4,7