Dominoes

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Dominoes is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Take a box of dominoes give them a good shuffle and then arrange them in diverse orientations such that they form a rectangle with 7 rows of 8 columns. Make a tableau of the face values e.g.

       05132231
       05505246
       43036620
       06235126
       11300245
       21433466
       64515414

Now torment your computer by making it identify where each domino is.

Do this for the above tableau and one of your own construction.

Extra credit:

How many ways are there to arrange dominoes in an 8x7 rectangle, first ignoring their values, then considering their values, and finally considering values but ignoring value symmetry, i.e. transposing 5 and 4.

F#

<lang fsharp> // Dominoes: Nigel Galloway. November 17th., 2021. let cP (n:seq<uint64 list * uint64>) g=seq{for y,n in n do for g in g do let l=n^^^g in if n+g=l then yield (g::y,l)} let rec fG n g=match g with h::t->fG(cP n h)t |_->fst(Seq.head n) let solve(N:int[])=let fG=let y=fG [([],0UL)]([for g in 0..47->((N.[g],N.[g+8]),(1UL<<<g)+(1UL<<<g+8))]@[for n in 0..6 do for g in n*8..n*8+6->((N.[g],N.[g+1]),(1UL<<<g)+(1UL<<<g+1))]

                               |>List.groupBy(fun((n,g),_)->(min n g,max n g))|>List.sort|>List.map(fun(_,n)->n|>List.map(fun(n,g)->g))) in (fun n g->if List.contains((1UL<<<n)+(1UL<<<g)) y then "+" else " ")
                  N|>Array.chunkBySize 8|>Array.iteri(fun n g->let n=n*8 in [0..6]|>List.iter(fun y->printf $"%d{g.[y]}%s{fG(n+y)(n+y+1)}"); printfn $"%d{g.[7]}"; [0..7]|>List.iter(fun g->printf $"%s{fG(n+g)(n+g+8)} "); printfn "")

solve [|0;5;1;3;2;2;3;1;

       0;5;5;0;5;2;4;6;
       4;3;0;3;6;6;2;0;
       0;6;2;3;5;1;2;6;
       1;1;3;0;0;2;4;5;
       2;1;4;3;3;4;6;6;
       6;4;5;1;5;4;1;4|]

</lang>

Output:

0+5 1+3 2 2+3 1
        +     +
0 5+5 0 5 2+4 6
+     +
4 3 0 3 6+6 2 0
  + +       + +
0 6 2 3+5 1 2 6
+         +
1 1 3 0+0 2 4 5
  + +       + +
2 1 4 3+3 4 6 6
+         +
6 4+5 1+5 4 1+4

<lang fsharp> solve [|5;6;2;0;0;4;1;4;

       3;6;1;3;0;4;2;2;
       3;5;6;4;3;2;1;1;
       3;5;1;1;3;0;0;5;
       6;0;5;4;3;5;5;2;
       4;4;1;3;6;6;0;2;
       1;2;6;2;6;5;0;4|]

</lang>

Output:

5+6 2+0 0 4 1+4
        + +
3+6 1 3 0 4 2+2
    + +
3 5 6 4 3+2 1 1
+ +         + +
3 5 1+1 3+0 0 5

6 0 5+4 3+5 5+2
+ +
4 4 1+3 6 6+0 2
        +     +
1+2 6+2 6 5+0 4