[wolfgang]

Put numbers( 1 to 9 )instead of the letters to make this equation correct:

AB/CD + EF/GHI = I

Hint:

I=C+G+H

E=B+D

A+F=E+H

[Guest]

I got more than a few answers, I'm a bit dozed to try them all but I'm pretty sure my solution:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[curr3nt]

I got more than a few answers, I'm a bit dozed to try them all but I'm pretty sure my solution:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

6 <= I <= 9 from I=C+G+H

I != 9 because largest value of AB/CD is 98/12 = 8.17 but if 1 is taken then EF/GHI can not be greater than .5 so I can't reach 9

C = 1 because largest value of AB/CD would be 98/21 = 4.67 which can't be made to equal the minimum of I from EF/GHI

None of your answers have C = 1

I am assuming that AB is actually equal to A*10+B not A * B.

Having a hard time working the other numbers around C = 1 and 6 <= I <= 8.

[Guest]

Clarification question:

Does AB mean a two-digit number AB, or does it mean A times B? Same applies for CD, EF, and GHI.

[curr3nt]

with C = 1

I != 6 because

then G and H would have to be 2 and 3 from I = C+G+H

means B and D have to be 4 and 5 making E = 9 from E = B+D

A and F would have to be 7 and 8

from A+F = E+H we have E+H = to 9+2 or 9+3 => 11 or 12 and A+F = 15

If I = 7

then G and H would have to be 2 and 4 from I = C+G+H

B and D could be 3 and 5 or 3 and 6 making E = 8 or 9

A and F would have to be 6 and 9 if (3|5) or 5 and 8 if (3|6)

from A+F = E+H we have

E+H = 8+2 or 8+4 = 15 - This can't happen

E+H = 9+2 or 9+4 = 13 - 9+4=5+8

from this we get

A=8

B=6

C=1

D=3

E=9

F=5

G=2

H=4

I=7

which is 86/13 + 95/247 = 7

[Guest]

72/84 + 93/651 = 1; 86/13 + 95/247 = 7; 87/93 + 42/651 = 1; 98/56 + 43/172 = 2

[Guest]

72/84 + 93/651 = 1; 86/13 + 95/247 = 7; 87/93 + 42/651 = 1; 98/56 + 43/172 = 2

Oh it's supposed to equal I, I knew there was something wrong cause I calculated it to be 1, in that case:

You're right, 4 possible situations:

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

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

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

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

Edited April 7, 2011 by Anza Power

[wolfgang]

Clarification question:

Does AB mean a two-digit number AB, or does it mean A times B? Same applies for CD, EF, and GHI.

AB...means...A*10+B

and the same for others.

[wolfgang]

with C = 1

I != 6 because

then G and H would have to be 2 and 3 from I = C+G+H

means B and D have to be 4 and 5 making E = 9 from E = B+D

A and F would have to be 7 and 8

from A+F = E+H we have E+H = to 9+2 or 9+3 => 11 or 12 and A+F = 15

If I = 7

then G and H would have to be 2 and 4 from I = C+G+H

B and D could be 3 and 5 or 3 and 6 making E = 8 or 9

A and F would have to be 6 and 9 if (3|5) or 5 and 8 if (3|6)

from A+F = E+H we have

E+H = 8+2 or 8+4 = 15 - This can't happen

E+H = 9+2 or 9+4 = 13 - 9+4=5+8

from this we get

A=8

B=6

C=1

D=3

E=9

F=5

G=2

H=4

I=7

which is 86/13 + 95/247 = 7

Wooooooooooooow !!!...Great

[wolfgang]

Oh it's supposed to equal I, I knew there was something wrong cause I calculated it to be 1, in that case:

You're right, 4 possible situations:

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

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

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

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

No...only one soultion is right...the others are wrong.

The second possibility is correct.