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Colorful Integral (Posted on 2009-07-06) Difficulty: 2 of 5
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    
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Solution 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        integral
1  2  4       .2916666666666667
1  2  5       .234375
1  3  4       .3209876543209876
1  4  3       .46875
1  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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