15 replies to this topic

[rookie1ja]

No. 1 - Back to the Cryptograms and Algebra Puzzles
Replace the same characters by the same numerals so that the mathematical operations are correct.

ABCB - DEFC = GAFB		
   :	  +	  -
  DH x   AB =  IEI
----------------------
 GGE  + DEBB = DHDG

This old topic is locked since solution is already provided in the Spoiler below.
Pls visit New Puzzles section to see always fresh brain teasers.

Spoiler for Solution

No. 1 - solution
A=3, B=8, C=0, D=1, E=4, F=5, G=2, H=7, I=6

3808  -  1450  =  2358
   :		+		-
  17  x	38  =   646
-------------------------
 224   +  1488  =  1712

[jonasguy13]

well I now know the answer to the problem but I would really love to see the solution to this problem and by that I mean I would like to see how the value of the variables was determined without just inputing random numbers.

[Wink79]

Here's how I attempted it:

C=0 is quite obvious from the ***B - ***C = ***B.

From the same summation, it is seen that as C=0, F must be 5 as C carries from B and becomes 10 and then subtract that from 5 gets 5. so F=5.

As 1 was carried from B, so (B-1) - E = A and also A + F = B. So we know from this that F= 1 + E. Hence E = 4.

Then from GAFB - IEI = DHDG, it is clear that A has carried from G so G - 1 = D. Hence G = D + 1 i.e. G = 2.

A - D = G so A = 3 and putting this in A + F = B, you can get B = 8.

I am sure you can take it from here

[cuendillar]

I'm new but I just had to ask...

Quoted from above:
"Then from GAFB - IEI = DHDG, it is clear that A has carried from G so G - 1 = D. Hence G = D + 1 i.e. G = 2."

I'm not sure you can say that with certainty. Where did you deduce D = 1 from? If you got it from
GAFB - IEI = DHDG then you made the assumption that B > I in B - I = G and it did not borrow from F in the next column to make the subtraction. If thats how you thought it through then how did you know that you could safely make that assumption?

[cjoshua_alba]

I did not get it

[haroliano]

Try with that:
Since ABCB : DH = GGE, and C = 0 and E = 4, B must be an even number.
But B must be greater than 5 (B=5+A), then you have only the 6 and the 8.
If B = 6, from the bottom 4+B=10, then G=0, but C=0, then don't works.
If B = 8, 4+B=12, then G=2.
Best Regards,
Harold
(I appologize for my bad english)

[bob]

a and b equals mc2 so you minus d from the entire equation and add pie which gives you a strange decimal. change the decimal to a fraction, add 3/4 and then divide by 7. you sould have the answer, if it's another decimal just round it to the nearest whole number and divide by c. you get c by multiplying d by b and then cross canceling out a which equals a number between one and 20. then you can easily get the final answer

[jk_iitk]

One Possible sol for ABCB-DEFC = GAFB
is
A=4
B=7
C=0
D=1
E=2
F=5
G=3

[jade_luvs_twilight]

A=3, B=8, C=0, D=1, E=4, F=5, G=2, H=7, I=6

[HRX]

I found alternate solutions to each one:

For #1: A=8,B=6,C=0,D=3,E=7,F=5,G=4
Thus: 8606+3750=4856

For #2: 52*13=676

For #: 6744+117=6861

My method was a combination of deduction and trial and error.