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 Back to the Wall (Posted on 2010-04-28)

No! Not a firing squad nor the need for a continuous line to cross all line segments just once!

To each vertex labeled A to L apply a different value from 1 to 12. Let V, W, X, Y and Z be the sums of their respective surrounding vertices.

Provide at least one example where V=W=X=Y=Z, or offer a reason why this, like the continuous line, is impossible.

 See The Solution Submitted by brianjn No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(2): computer solution -- the program | Comment 3 of 17 |
(In reply to re: computer solution -- the part that got cut off by Charlie)

OPEN "backwall.txt" FOR OUTPUT AS #2
DIM SHARED used(12)
CLS
FOR a = 1 TO 11
IF used(a) = 0 THEN
used(a) = 1
FOR b = 1 TO 12
IF used(b) = 0 THEN
used(b) = 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
v = a + b + e + f
FOR d = a + 1 TO 12
IF used(d) = 0 THEN
used(d) = 1
FOR c = 1 TO 12
IF used(c) = 0 THEN
used(c) = 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
x = c + d + h + i
IF x = v THEN
FOR g = 1 TO 12
IF used(g) = 0 THEN
used(g) = 1
w = b + c + f + g + h
IF w = x THEN
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
y = e + f + g + j + k
IF y = w THEN
FOR l = 1 TO 12
IF used(l) = 0 THEN
used(l) = 1
z = g + h + i + k + l
IF z = y THEN
PRINT a; b; c; d: PRINT e; f; g; h; i: PRINT j; k; l
PRINT v; w; x; y; z: PRINT
PRINT #2, a; b; c; d: PRINT #2, e; f; g; h; i: PRINT #2, j; k; l
PRINT #2, v; w; x; y; z: PRINT #2,
ct = ct + 1
END IF
used(l) = 0
END IF
NEXT
END IF
used(k) = 0
END IF
NEXT
used(j) = 0
END IF
NEXT
END IF
used(g) = 0
END IF
NEXT
END IF
used(i) = 0
END IF
NEXT
used(h) = 0
END IF
NEXT
used(c) = 0
END IF
NEXT
used(d) = 0
END IF
NEXT
used(f) = 0
END IF
NEXT
used(e) = 0
END IF
NEXT
used(b) = 0
END IF
NEXT
used(a) = 0
END IF
NEXT
PRINT ct: PRINT #2, ct

 Posted by Charlie on 2010-04-28 13:53:06

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