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Firstly, in offering this as a problem I set out to test if my proposal could be substantiated since the classic continuous line was an impossibility. As such I required just one solution to prove possibility.
Secondly, please take the following comments in context with the comments in the forum.
The early discussion [first 5 comments] has been made on a misinterpretation of intent. The original proposal was clearly about rectangles
and not polygons ('pentagons' in this case).
There is a dirth of solutions with "1" in position "A" with each 'brick' having a total of 25, 27, 28 or 29.
I ran my computer overnight but it went into "Hibernation" soon after I left it! (My QuickBASIC and his, as I understand are of different versions and mine running on a slower CPU.)
Charlie has done a revamp across 4 pages in line with my intention. I cannot doubt his claim that 23 and 24 are also sums for the rectangles as they provide a balance around 26 which he claims does not exist and I didn't find in my meagre searches.
1 3 5 4 12 11 2 8 10 7 6 9 27
1 3 5 4 12 11 6 8 10 7 2 9 27
1 3 8 4 12 11 2 5 10 7 6 9 27
1 3 8 4 12 11 6 5 10 7 2 9 27
1 4 2 5 10 12 3 9 11 8 6 7 27
1 4 2 5 10 12 6 9 11 8 3 7 27
1 4 2 6 12 10 3 11 8 5 7 9 27
1 4 2 6 12 10 7 11 8 5 3 9 27
1 4 2 7 11 12 6 10 9 3 8 5 28
1 4 2 7 11 12 8 10 9 3 6 5 28
1 4 2 8 12 10 5 11 6 3 7 9 27
1 4 2 8 12 10 7 11 6 3 5 9 27
1 4 2 10 8 12 3 7 6 9 5 11 25
1 4 2 10 8 12 5 7 6 9 3 11 25
1 4 3 7 12 11 5 10 8 2 9 6 28
1 4 3 7 12 11 9 10 8 2 5 6 28
1 4 3 9 8 12 2 6 7 10 5 11 25
1 4 3 9 8 12 5 6 7 10 2 11 25
1 4 3 10 9 11 2 7 5 8 6 12 25
1 4 3 10 9 11 6 7 5 8 2 12 25
1 4 3 11 10 12 6 8 5 2 9 7 27
1 4 3 11 10 12 9 8 5 2 6 7 27
1 4 6 3 12 10 2 7 11 8 5 9 27
1 4 6 3 12 10 5 7 11 8 2 9 27
1 4 6 9 8 12 2 3 7 10 5 11 25
1 4 6 9 8 12 5 3 7 10 2 11 25
1 4 7 3 12 10 2 6 11 8 5 9 27
1 4 7 3 12 10 5 6 11 8 2 9 27
1 4 7 10 8 12 3 2 6 9 5 11 25
1 4 7 10 8 12 5 2 6 9 3 11 25
1 4 7 10 9 11 2 3 5 8 6 12 25
1 4 7 10 9 11 6 3 5 8 2 12 25
1 4 8 11 10 12 6 3 5 2 9 7 27
1 4 8 11 10 12 9 3 5 2 6 7 27
1 4 9 5 10 12 3 2 11 8 6 7 27
1 4 9 5 10 12 6 2 11 8 3 7 27
1 4 10 7 11 12 6 2 9 3 8 5 28
1 4 10 7 11 12 8 2 9 3 6 5 28
1 4 10 7 12 11 5 3 8 2 9 6 28
1 4 10 7 12 11 9 3 8 2 5 6 28
1 4 11 6 12 10 3 2 8 5 7 9 27
1 4 11 6 12 10 7 2 8 5 3 9 27
1 4 11 8 12 10 5 2 6 3 7 9 27
1 4 11 8 12 10 7 2 6 3 5 9 27
1 5 2 9 7 12 3 6 8 11 4 10 25
1 5 2 9 7 12 4 6 8 11 3 10 25
1 5 2 10 9 12 3 8 7 4 11 6 27
1 5 2 10 9 12 11 8 7 4 3 6 27
1 5 2 11 9 10 3 8 4 7 6 12 25
1 5 2 11 9 10 6 8 4 7 3 12 25
1 5 3 4 10 11 2 8 12 9 6 7 27
1 5 3 4 10 11 6 8 12 9 2 7 27
1 5 4 7 9 10 2 6 8 11 3 12 25
1 5 4 7 9 10 3 6 8 11 2 12 25
1 5 4 7 12 10 3 9 8 2 11 6 28
1 5 4 7 12 10 11 9 8 2 3 6 28
1 5 6 7 9 10 2 4 8 11 3 12 25
1 5 6 7 9 10 3 4 8 11 2 12 25
1 5 6 9 7 12 3 2 8 11 4 10 25
1 5 6 9 7 12 4 2 8 11 3 10 25
1 5 8 4 10 11 2 3 12 9 6 7 27
1 5 8 4 10 11 6 3 12 9 2 7 27
1 5 8 10 9 12 3 2 7 4 11 6 27
1 5 8 10 9 12 11 2 7 4 3 6 27
1 5 8 11 9 10 3 2 4 7 6 12 25
1 5 8 11 9 10 6 2 4 7 3 12 25
1 5 9 7 12 10 3 4 8 2 11 6 28
1 5 9 7 12 10 11 4 8 2 3 6 28
1 6 2 4 12 8 3 11 10 7 5 9 27
1 6 2 4 12 8 5 11 10 7 3 9 27
1 6 2 7 9 12 4 8 11 5 10 3 28
1 6 2 7 9 12 10 8 11 5 4 3 28
1 6 3 8 7 11 2 5 9 12 4 10 25
1 6 3 8 7 11 4 5 9 12 2 10 25
1 6 4 5 12 10 7 9 11 2 8 3 29
1 6 4 5 12 10 8 9 11 2 7 3 29
1 6 4 7 8 10 2 5 9 12 3 11 25
1 6 4 7 8 10 3 5 9 12 2 11 25
1 6 4 7 11 10 2 8 9 3 12 5 28
1 6 4 7 11 10 12 8 9 3 2 5 28
1 6 5 7 8 10 2 4 9 12 3 11 25
1 6 5 7 8 10 3 4 9 12 2 11 25
1 6 5 8 7 11 2 3 9 12 4 10 25
1 6 5 8 7 11 4 3 9 12 2 10 25
1 6 8 7 9 12 4 2 11 5 10 3 28
1 6 8 7 9 12 10 2 11 5 4 3 28
1 6 8 7 11 10 2 4 9 3 12 5 28
1 6 8 7 11 10 12 4 9 3 2 5 28
1 6 9 5 12 10 7 4 11 2 8 3 29
1 6 9 5 12 10 8 4 11 2 7 3 29
1 6 11 4 12 8 3 2 10 7 5 9 27
1 6 11 4 12 8 5 2 10 7 3 9 27
1 7 2 4 11 9 3 10 12 6 8 5 28
1 7 2 4 11 9 8 10 12 6 3 5 28
1 7 2 5 12 8 3 11 10 4 9 6 28
1 7 2 5 12 8 9 11 10 4 3 6 28
1 7 3 4 12 8 2 10 11 5 9 6 28
1 7 3 4 12 8 9 10 11 5 2 6 28
1 7 3 9 8 12 5 6 10 4 11 2 28
1 7 3 9 8 12 11 6 10 4 5 2 28
1 7 4 5 11 10 6 8 12 3 9 2 29
1 7 4 5 11 10 9 8 12 3 6 2 29
1 7 4 10 8 12 6 5 9 3 11 2 28
1 7 4 10 8 12 11 5 9 3 6 2 28
1 7 4 10 9 11 5 6 8 2 12 3 28
1 7 4 10 9 11 12 6 8 2 5 3 28
1 7 5 10 8 12 6 4 9 3 11 2 28
1 7 5 10 8 12 11 4 9 3 6 2 28
1 7 6 9 8 12 5 3 10 4 11 2 28
1 7 6 9 8 12 11 3 10 4 5 2 28
1 7 6 10 9 11 5 4 8 2 12 3 28
1 7 6 10 9 11 12 4 8 2 5 3 28
1 7 8 5 11 10 6 4 12 3 9 2 29
1 7 8 5 11 10 9 4 12 3 6 2 29
1 7 10 4 11 9 3 2 12 6 8 5 28
1 7 10 4 11 9 8 2 12 6 3 5 28
1 7 10 4 12 8 2 3 11 5 9 6 28
1 7 10 4 12 8 9 3 11 5 2 6 28
1 7 11 5 12 8 3 2 10 4 9 6 28
1 7 11 5 12 8 9 2 10 4 3 6 28
1 8 2 4 12 6 3 11 10 7 5 9 27
1 8 2 4 12 6 5 11 10 7 3 9 27
1 8 2 5 12 7 3 11 10 4 9 6 28
1 8 2 5 12 7 9 11 10 4 3 6 28
1 8 3 4 12 7 2 10 11 5 9 6 28
1 8 3 4 12 7 9 10 11 5 2 6 28
1 8 3 10 7 11 2 5 9 6 12 4 27
1 8 3 10 7 11 12 5 9 6 2 4 27
1 8 4 7 9 10 2 6 11 5 12 3 28
1 8 4 7 9 10 12 6 11 5 2 3 28
1 8 5 10 7 11 2 3 9 6 12 4 27
1 8 5 10 7 11 12 3 9 6 2 4 27
1 8 6 7 9 10 2 4 11 5 12 3 28
1 8 6 7 9 10 12 4 11 5 2 3 28
1 8 10 4 12 7 2 3 11 5 9 6 28
1 8 10 4 12 7 9 3 11 5 2 6 28
1 8 11 4 12 6 3 2 10 7 5 9 27
1 8 11 4 12 6 5 2 10 7 3 9 27
1 8 11 5 12 7 3 2 10 4 9 6 28
1 8 11 5 12 7 9 2 10 4 3 6 28
1 9 2 4 11 7 3 10 12 6 8 5 28
1 9 2 4 11 7 8 10 12 6 3 5 28
1 9 2 11 7 10 3 6 8 5 12 4 27
1 9 2 11 7 10 12 6 8 5 3 4 27
1 9 4 7 8 10 3 5 12 6 11 2 28
1 9 4 7 8 10 11 5 12 6 3 2 28
1 9 5 7 8 10 3 4 12 6 11 2 28
1 9 5 7 8 10 11 4 12 6 3 2 28
1 9 6 11 7 10 3 2 8 5 12 4 27
1 9 6 11 7 10 12 2 8 5 3 4 27
1 9 10 4 11 7 3 2 12 6 8 5 28
1 9 10 4 11 7 8 2 12 6 3 5 28
1 10 2 6 12 4 3 11 8 5 7 9 27
1 10 2 6 12 4 7 11 8 5 3 9 27
1 10 2 8 12 4 5 11 6 3 7 9 27
1 10 2 8 12 4 7 11 6 3 5 9 27
1 10 2 11 7 9 3 6 8 5 12 4 27
1 10 2 11 7 9 12 6 8 5 3 4 27
1 10 2 11 9 5 3 8 4 7 6 12 25
1 10 2 11 9 5 6 8 4 7 3 12 25
1 10 4 5 11 7 6 8 12 3 9 2 29
1 10 4 5 11 7 9 8 12 3 6 2 29
1 10 4 5 12 6 7 9 11 2 8 3 29
1 10 4 5 12 6 8 9 11 2 7 3 29
1 10 4 7 8 6 2 5 9 12 3 11 25
1 10 4 7 8 6 3 5 9 12 2 11 25
1 10 4 7 8 9 3 5 12 6 11 2 28
1 10 4 7 8 9 11 5 12 6 3 2 28
1 10 4 7 9 5 2 6 8 11 3 12 25
1 10 4 7 9 5 3 6 8 11 2 12 25
1 10 4 7 9 8 2 6 11 5 12 3 28
1 10 4 7 9 8 12 6 11 5 2 3 28
1 10 4 7 11 6 2 8 9 3 12 5 28
1 10 4 7 11 6 12 8 9 3 2 5 28
1 10 4 7 12 5 3 9 8 2 11 6 28
1 10 4 7 12 5 11 9 8 2 3 6 28
1 10 5 7 8 6 2 4 9 12 3 11 25
1 10 5 7 8 6 3 4 9 12 2 11 25
1 10 5 7 8 9 3 4 12 6 11 2 28
1 10 5 7 8 9 11 4 12 6 3 2 28
1 10 6 3 12 4 2 7 11 8 5 9 27
1 10 6 3 12 4 5 7 11 8 2 9 27
1 10 6 7 9 5 2 4 8 11 3 12 25
1 10 6 7 9 5 3 4 8 11 2 12 25
1 10 6 7 9 8 2 4 11 5 12 3 28
1 10 6 7 9 8 12 4 11 5 2 3 28
1 10 6 11 7 9 3 2 8 5 12 4 27
1 10 6 11 7 9 12 2 8 5 3 4 27
1 10 7 3 12 4 2 6 11 8 5 9 27
1 10 7 3 12 4 5 6 11 8 2 9 27
1 10 8 5 11 7 6 4 12 3 9 2 29
1 10 8 5 11 7 9 4 12 3 6 2 29
1 10 8 7 11 6 2 4 9 3 12 5 28
1 10 8 7 11 6 12 4 9 3 2 5 28
1 10 8 11 9 5 3 2 4 7 6 12 25
1 10 8 11 9 5 6 2 4 7 3 12 25
1 10 9 5 12 6 7 4 11 2 8 3 29
1 10 9 5 12 6 8 4 11 2 7 3 29
1 10 9 7 12 5 3 4 8 2 11 6 28
1 10 9 7 12 5 11 4 8 2 3 6 28
1 10 11 6 12 4 3 2 8 5 7 9 27
1 10 11 6 12 4 7 2 8 5 3 9 27
1 10 11 8 12 4 5 2 6 3 7 9 27
1 10 11 8 12 4 7 2 6 3 5 9 27
1 11 3 4 10 5 2 8 12 9 6 7 27
1 11 3 4 10 5 6 8 12 9 2 7 27
1 11 3 7 12 4 5 10 8 2 9 6 28
1 11 3 7 12 4 9 10 8 2 5 6 28
1 11 3 8 7 6 2 5 9 12 4 10 25
1 11 3 8 7 6 4 5 9 12 2 10 25
1 11 3 10 7 8 2 5 9 6 12 4 27
1 11 3 10 7 8 12 5 9 6 2 4 27
1 11 3 10 9 4 2 7 5 8 6 12 25
1 11 3 10 9 4 6 7 5 8 2 12 25
1 11 4 10 9 7 5 6 8 2 12 3 28
1 11 4 10 9 7 12 6 8 2 5 3 28
1 11 5 4 12 3 2 8 10 7 6 9 27
1 11 5 4 12 3 6 8 10 7 2 9 27
1 11 5 8 7 6 2 3 9 12 4 10 25
1 11 5 8 7 6 4 3 9 12 2 10 25
1 11 5 10 7 8 2 3 9 6 12 4 27
1 11 5 10 7 8 12 3 9 6 2 4 27
1 11 6 10 9 7 5 4 8 2 12 3 28
1 11 6 10 9 7 12 4 8 2 5 3 28
1 11 7 10 9 4 2 3 5 8 6 12 25
1 11 7 10 9 4 6 3 5 8 2 12 25
1 11 8 4 10 5 2 3 12 9 6 7 27
1 11 8 4 10 5 6 3 12 9 2 7 27
1 11 8 4 12 3 2 5 10 7 6 9 27
1 11 8 4 12 3 6 5 10 7 2 9 27
The following is my program listing, which other than values for W, Y and Z in Charlie's program, is very similar to his having been built on a model which he so often uses.
CLS
DIM used(15)
OPEN "WALL.TXT" FOR OUTPUT AS #1
FOR a = 1 TO 12
IF used(a) = 0 THEN
used(a) = 1
FOR b = 1 TO 12
IF used(b) = 0 THEN
used(b) = 1
FOR c = 1 TO 12
IF used(c) = 0 THEN
used(c) = 1
FOR d = 1 TO 12
IF used(d) = 0 THEN
used(d) = 1
FOR e = 1 TO 12
IF used(e) = 0 THEN
used(e) = 1
FOR f = 1 TO 12
IF used(f) = 0 THEN
used(f) = 1
FOR g = 1 TO 12
IF used(g) = 0 THEN
used(g) = 1
FOR h = 1 TO 12
IF used(h) = 0 THEN
used(h) = 1
FOR i = 1 TO 12
IF used(i) = 0 THEN
used(i) = 1
FOR j = 1 TO 12
IF used(j) = 0 THEN
used(j) = 1
FOR k = 1 TO 12
IF used(k) = 0 THEN
used(k) = 1
FOR l = 1 TO 12
IF used(l) = 0 THEN
used(l) = 1
v = a + b + e + f
w = b + c + f + h
x = c + d + h + i
y = e + g + j + k
z = g + i + k + l
LOCATE 1, 1: PRINT a; b; c; d; e; f; g; h; i; j; k; l, v; w; x; y; z
IF v = w AND w = x AND x = y AND y = z THEN
PRINT a; b; c; d; e; f; g; h; i; j; k; l, v
PRINT #1, a; b; c; d; e; f; g; h; i; j; k; l, v
END IF
used(l) = 0
END IF
NEXT
used(k) = 0
END IF
NEXT
used(j) = 0
END IF
NEXT
used(i) = 0
END IF
NEXT
used(h) = 0
END IF
NEXT
used(g) = 0
END IF
NEXT
used(f) = 0
END IF
NEXT
used(e) = 0
END IF
NEXT
used(d) = 0
END IF
NEXT
used(c) = 0
END IF
NEXT
used(b) = 0
END IF
NEXT
used(a) = 0
END IF
NEXT
CLOSE 1
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