(I) ABBC : DDE = DF
+ + *
(II) AGFG - AHIB = KKG
----------------------
(III) KGEH + ACKE = FCII
(IV) (V) (VI)
Solution:
(V.1) B = 0
(III*) K + A <= F
(II.2) K + I = F as K < F
(II.3) K + H = G
(IV.2) F + 1 = E
(IV.1) C + G = H + 10
(II.3)+(IV.1) K + C = 10
(IV.4) 2 A = K
(III*)+(IV.4)+(IV.2) 3A+1 <= E <= 9 => A <= 2
(I) D * D <= A <= 2 => D = 1 and A = 2
(V.2) I + 1 = K
(V.3) H + 1 = C
(IV.1)+(V.3) G = 9
Then we get the remaining variables
K = 2A = 4, I = 2A-1 = 3, F = 4A-1 = 7, E = 4A, C = 10-2A = 6, H = 9-2A = 5.
2006 : 118 = 17
+ + *
2979 - 2530 = 449
----------------------
4985 + 2648 = 7633
References:
Hoer Zu, No 29, 2003-07-11