(I) ABCD + DCEF = GHFI
- : +
(II) AHGE + AIC = AKGF
----------------------
(III) KEG * KI = EBKB
(IV) (V) (VI)
Solution:
(III) K * K <= E
Therefore K <= 3. Assume K = 3 then E = 9
but then (III) were 39 * 3 > 100 which is impossible.
Otherwise there is a lower bound for K.
(II.3) H + A <= K (and A not zero)
So we have two numbers lower than K. Therefore
H=0, A=1, K=2.
(IV.3) shows B = 3.
(VI.4) E = G + 1
(I.4) 1 + D + 1 = G (we have a carry)
(IV.1) G + E = D + 10 (G > D)
Solving these three equation gives
D=5, G=7, E=8.
(IV.1) G + E + 1 = C + 10
C=6
(II.2) E + C = 10 + F
F=4
(I.1) D + F = I
I=9
1365 + 5684 = 7049
- : +
1078 + 196 = 1274
----------------------
287 * 29 = 8323
References:
Hoer Zu, No 31, 2003-07-25