# Letter Sum #4

Rating: hard

### Instructions:

Each letter in the given sum represents a different digit (0-9). Figure out which letter represents which digit so that the given addition is correct. No number is written with 0 as its first digit.

`    A B C D A F`
`+   B G E D E H`

`  C E C C B F A`
`    A B C D A F`
`+   B G E D E H`

`  C E C C B F A`
`    5 4 1 2 5 6`
`+   4 7 0 2 0 9`

`  1 0 1 1 4 6 5`

Notes on solution, by puzzle editor:

This one is actually not so hard. First you see that C=1, then note from the fourth column (from the right) that E is 0 or 9 (depending upon whether there’s a carry from the third column). You can't make the sixth column work out if E is 9, so it must be 0, and A+B=9.

Now you know that H=9 and there's no carry into the third column, so B is even, A=9-B is odd, F=A+1, G=A+2. Since 1 and 9 are already assigned, A and G can only be 3 and 5 or 5 and 7. If A is 3, then B is 6 (sixth column) and D is 3 (third column). That's a clash, so A=5, B=4, D=2, F=6, G=7.