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

C
∫ x^-S dx = .COLORS
A

The integral will evaluate to 1/(4a^4) - 1/(4c^4). The following program evaluates this for the possible values of a anc c. If the result falls between c/10 and (c+1)/10, it is printed:

DEFDBL A-Z
FOR a = 1 TO 9
FOR c = 1 TO 9
 v = 1 / (4 * a * a * a * a) - 1 / (4 * c * c * c * c)
 IF v >= c / 10 AND v < (c + 1) / 10 THEN PRINT a; c, v
NEXT
NEXT

Only one such integral falls in the range required by c, in which a is 1, c is 2, and the integral comes out to .234375, which fits the pattern of .colors.

S, at 5, is in fact >= 2, but that constraint was not needed within the program.

Posted by Charlie on 2009-07-06 16:52:14