Solve this alphametic integral puzzle, where each of the capital letters in bold represents a different decimal digit from 0 to 9, given that C and N are constants and, E is not zero.

B
∫ C*x^N dx = EDGE
A

A=0, B=6, C=8, N=3, EDGE = 2592

Integ{0..6} 8x^3 dx = 2592

as Integ{A..B} C*x^N dx = C * (B^(N + 1) - A^(N + 1)) / (N + 1):

FOR a = 0 TO 9
 used(a) = 1
FOR b = 0 TO 9
IF used(b) = 0 THEN
 used(b) = 1
FOR c = 0 TO 9
IF used(c) = 0 THEN
 used(c) = 1
FOR n = 0 TO 9
IF used(n) = 0 THEN
 used(n) = 1

 num = INT(c * (b ^ (n + 1) - a ^ (n + 1)) + .5)
 den = n + 1
 edge = num / den
 IF edge = INT(edge) AND edge > 1000 AND edge < 10000 THEN
   IF edge \ 1000 = edge MOD 10 THEN
    e = edge MOD 10
    d = (edge \ 100) MOD 10
    g = (edge \ 10) MOD 10
    IF used(e) = 0 AND used(d) = 0 AND used(g) = 0 THEN
      IF e <> d AND d <> g AND e <> g THEN
       PRINT a; b; c, n, edge
      END IF
    END IF
   END IF
 END IF

 used(n) = 0
END IF
NEXT
 used(c) = 0
END IF
NEXT
 used(b) = 0
END IF
NEXT
 used(a) = 0
NEXT

 

Posted by Charlie on 2009-03-25 13:44:35