Substitute each of the capital letters in bold by a different digit from 0 to 9 to satisfy this alphametic equation. Neither W nor S is zero and T ≥ 2.

W
∫ x^-T dx = .WORLD
S

Integ{1 to 4} x ^ -3 dx = .46875

based on

1  4  3       .46875

from

DEFDBL A-Z
FOR t = 2 TO 9
 IF used(t) = 0 THEN
  used(t) = 1
FOR s = 1 TO 9
 IF used(s) = 0 THEN
  used(s) = 1
  term2 = s ^ (1 - t) ' numerator of antiderivative at s
FOR w = 1 TO 9
 IF used(w) = 0 THEN
  used(w) = 1
  term1 = w ^ (1 - t) ' numerator of antiderivative at w
FOR o = 0 TO 9
 IF used(o) = 0 THEN
  used(o) = 1
FOR r = 0 TO 9
 IF used(r) = 0 THEN
  used(r) = 1
FOR l = 0 TO 9
 IF used(l) = 0 THEN
  used(l) = 1
FOR d = 0 TO 9
 IF used(d) = 0 THEN
  used(d) = 1

  world = w / 10# + o / 100# + r / 1000# + l / 10000# + d / 100000#
  IF term1 - term2 = world * (1 - t) THEN ' denominator introduced here
     PRINT s; w; t, world
  END IF

  used(d) = 0
 END IF
NEXT
  used(l) = 0
 END IF
NEXT
  used(r) = 0
 END IF
NEXT
  used(o) = 0
 END IF
NEXT
  used(w) = 0
 END IF
NEXT
  used(s) = 0
 END IF
NEXT
  used(t) = 0
 END IF
NEXT

 

Posted by Charlie on 2009-09-15 21:51:52