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,
.
Puzzle 2
Puzzle 3
