# Letter Sum #2

Rating: easy

### 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 A`
`+   E C E E B`

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

`  E D E C F E`
`  7 1 9 0 7 7`
`+   8 9 8 8 1`

`  8 0 8 9 5 8`

Notes on solution, by puzzle editor:

You'll immediately note that there must be a carry into the leading (leftmost) column, since A and E must be different digits. So E=A+1. Turning your eye to the first (rightmost) column, clearly B=1 (since E=A+1 and E=A+B). And neither A nor E are 0 since numbers aren't written with leading zeros; A must be less than 9 given the rightmost column where E is not zero and therefore A+1 < 10 and A+1=E.

Going back to the fifth column from the right, we now have that either 1+E=10+D (if there's no carry into this column from the fourth column) or 2+E=10+D (if there is a carry), to get a carry into the leading column. D can't be 1, since B=1, so D must be 0, and E is 8 or 9, and A is 7 or 8.

Now the second column (from the right) is 7+8 or 8+9 and must give a carry to the third column. D being 0 (and C not being 0) we have 1+E=C. Hm, so if E=A+1 and C=E+1, and A is at least 7, then A=7, E=8, C=9. Fill all this in, discover that F=5 and you're done!