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.

(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