D-A=I & B-C=G & AC+IC=DE & FG-DE=HI (Hint C=4)?

Question

D-A=I & B-C=G & AC+IC=DE & FG-DE=HI (Hint C=4)

The numbers 1,2,3,4,5,6,7,8 & 9 can each be used to replace a letter but they an each ony replace one letter. Each number must be used. Where do I start? if C=4 than E should equal 8, now what????

It is an hour and 37 minutes past bedtime...Ugh!

Answer 1

D - A = I (Eqn. 1)
B - C = G (Eqn. 2)
AC + IC = DE (Eqn. 3)
FG - DE = HI (Eqn. 4)

Given hint: C = 4

Oh... sorry, I misunderstood your question...

A = 1
B = 7
C = 4
D = 6
E = 8
F = 9
G = 3
H = 2
I = 5

6 - 1 = 5
7 - 4 = 3
14 + 54 = 68
93 - 68 = 25

Night-night! Get some sleep now, okay? =)

Answer 2

We're given 5 expressions:
(i) D - A = I
(ii) B - C = G
(iii) AC + IC = DE
(iv) FG - DE = HI
(v) * C = 4

We already know that C = 4. From (iii) we also know that
* E = 8.

From (iv), we can determine that either:
I = G - E or I = (G + 10) - E
=> I = G - 8 or I = G + 10 - 8 = G + 2

From (ii), we know that G = B - 4, and that B > 4 (since G cannot be less than one)
From above: I = G - 8 or I = G + 2
=> I = B - 4 - 8 = B - 12 or I = B - 4 + 2 = B - 2
But 'I' cannot equal B - 12 because the highest number is 9, and 'I' cannot be negative. In other words,

(vi) I = G + 2 = B - 2

Now that we've confirmed that (G + 10) - E = I, we can also say that:

(vii) (F - 1) - D = H

From (vii), we can say that D < 8 (since F cannot be greater than 9). Since D < 8, we know from (i), that I < 7. From (vi), we know that I = G + 2, so: I > 2. This means that 'I' can only be 3, 4, 5, or 6. But,
'I' cannot equal 6, because then, B would be 8.
'I' cannot equal 4, because C = 4.

So 'I' can only equal 3 or 5.

But knowing that D < 8, there is no suitable value for D, if I = 3.

Therefore, * I = 5.
From (vi), we know that * B = 7, and * G = 3.

From (i), we know that D - A = I = 5.
We know from before that D < 8, and now we know that D > 5 (because there are no negatives), but D cannot equal 7 because B = 7.

This means that * D = 6. From (i), we can then determine that * A = 1.

The only numbers that are left are: 9, and 2. From (vii), we know that F - 7 = H, so * F = 9, and * H = 2.

Therefore,
A = 1
B = 7
C = 4
D = 6
E = 8
F = 9
G = 3
H = 2
I = 5