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 Colorful Integral (Posted on 2009-07-06)
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

 See The Solution Submitted by K Sengupta No Rating

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 re(3): computer solution -- corrected Comment 4 of 4 |
(In reply to re(2): computer solution by Charlie)

Given that S appears in the exponent on the LHS, the corrected program is:

DEFDBL A-Z
FOR a = 1 TO 9
FOR c = 1 TO 9
FOR s = 2 TO 9
vp = s - 1: vn = s - 1
FOR i = 1 TO s - 1
vp = vp * a: vn = vn * c
NEXT
v = 1 / vp - 1 / vn
IF v >= c / 10 AND v < (c + 1) / 10 THEN PRINT a; c; s, v
NEXT
NEXT
NEXT

It finds:

`A  C  S        integral1  2  4       .29166666666666671  2  5       .2343751  3  4       .32098765432098761  4  3       .468751  8  2       .875`

The only one of these that fits the pattern is for A = 1, C = 2 and S = 5.

 Posted by Charlie on 2009-07-07 11:33:28

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