Question

Each digit, 1, 2, 3, 4, 5, 6, 7, 8 and 9 is represented by a different letter A, B, C, D, E, F, G, H and I but not necessarily in this order. Further, each of A + B + C, C + D + E, E + F + G and G + H + I is equal to 13.

What is the sum of C ,E and G
Options
1) 7 2) 9 3) 11 4) Cannot be determined

How many different sum’s of A, D, F and I are possible?
Options
1) 1 2) 2 3) 4 4) Cannot be determined

Answer 1

C+E+G = 7

Answer 2

A + B + C = 13
C + D + E = 13
E + F + G = 13
G + H + I = 13

Adding all the above equations, we get
(A+B+C+D+E+G+H+I) + (C+E+G) = 13*4
So, (1+2+3+4+5+6+7+8+9) + (C+E+G) = 13*4
So, 9*10/2 + (C+E+G) = 52
So, (C+E+G) = 52-45 = 7

Answer 3

Yes, I same.

Answer 4

Can we determine the value of E???

Answer 5

Not quite same, I did 2(E+C +G) + 45- (E+C+G) = 52.

Answer 6

Let's see, I have

E + (E+C+G) + F +D = 26

E + F + D = 19

Answer 7

This just a question of messing around with the equations until u "see" a path.

Should be some matrix way of doing it, I guess.

Answer 8

I found all the triplets that added to 13 and got the following. May b that combined with one of your equations might help. The triplets are - (1,3,9); (1,4,8); (1,5,7); (2,3,8); (2,4,7); (2,5,6); (3,4,6)

Answer 9

Got it... So combining my triplets and your equations.
A = 9, B =3, C=1, D=8, E=4, F=7, G=2, H=5 and I =6. With these you can solve all the three questions you asked for :)