By: Yuliya Nesterova

Solutions to the Winter Puzzles in Issue 15 of Notes from the Margin.

## Puzzle 1

- Looking at the tens’ digit column, two evens, an odd, and a carried digit must sum to an odd digit. Therefore, the carried digit is a 2, and the ones’ column’s sum is between 21 and 29, inclusive.
- Likewise, in the ten thousdands’ digit column, the carried digit must be a 1, so (in the thousands’ column),
- Notice that the hundreds’ digit column has no carried digits from tens’ column addition: that is, , with .
- Working case-by-case (see below), we conclude that , , and is either or .
- Looking at the thousands’ and ten thousands’ digit column, implies , and since , must be . This is a contradiction, since and should be distinct digits.
- On the other hand, implies and, given that , must be }. .
- Completing the rest of the puzzle, , so , and since all letters are distinct, and . From here, we know that .
- By the process of elimination, .