1. The Power of Sudoku
I’ve been solving Sudoku puzzles for a few years now, moving from very easy to really
complex. I’m now working through a book of “Platinum” level puzzles, each of which takes me
around a week to solve (and I only successfully solve about half of them). After spending so
much of my free time on these simple numerical grids, I’ve begun to wonder if there might be
better ways to spend my time.
However, I realized this last weekend that solving Sudoku puzzles has helped me hone my
strategic thinking. I’ve developed some pretty sophisticated logic tools as my puzzle-solving
skills have grown. Let me illustrate with the routine I usually follow when starting a new Sudoku
puzzle:
1. Beginning from the top, look at the horizontal digits in the first three rows, comparing
which digits are in two of the rows but not all three rows. Check the row in which that
digit can’t be found to determine if there’s one and only one place that digit can go on
that row. If so, write in the digit.
2. Continue this strategy on the second three rows.
3. Move to the first column to the left, following the same steps as were followed
horizontally. This is the “low-hanging fruit” of the puzzle.
4. Move quickly through the horizontal rows again, in case any of the digits you filled in
vertically provided clues to help you solve the rows.
5. Beginning from the top left corner, check whether that group of nine squares has any
empty spaces in which one and only one digit will fit. If you find any like this, fill in the
appropriate digit.
6. Continue this strategy on the center-top group of nine squares, progressing through
each of the nine groups of nine squares each.

2. 7. Check whether there are any rows or columns in which eight of the nine squares are
filled in. If so, fill in the appropriate digit.
8. Next, look through each row to determine if any of them have only one space in which a
specific digit will work, moving 1-9. Once you determine that a digit can fit in more than
one space, move to the next digit. If you find a space in which only one particular digit
will work, fill in that digit and move to the next digit.
9. Next, make tiny notations in each empty square to remind you of which digits will work in
each one.
10. Examine the notations by row, column, and nine-square unit for patterns. One common
pattern is to find two squares in the same row or column that can only contain the same
two digits. Since one of those digits must be found in one of the two squares, both digits
can be eliminated as possibilities for any other square on that row, column, or nine-
square unit.
11. If all else fails, find a square for which there are only two possibilities, two digits that will
work. Fill in the digit that will cause the most change to the puzzle, and work out what
choosing that digit will mean for the other squares in that row, column, and nine-square
unit. You may find it helpful to do this on another sheet of paper – possibly graph paper,
since the grid is already filled in for you. Does the puzzle still work? If so, try choosing
the other digit – does it cause anything else in the puzzle to not work?
Such involved logic carries over to more meaningful areas of my life, such as my work. I
teach, among other subjects, query development in a sophisticated database. One of the
tools I give students is a query-planning form. This is simply a sheet with spaces for the
query name, purpose, fields, tables, joins, etc.
Learning to use some tool with which to plan queries helps students to get in the habit of
thinking systematically about answering questions of the database. Once a student has
used this or any written query-planning tool, he/she begins to think systematically about how
to build a logical question. This is done by asking smaller questions, such as:

3. 1. Has someone else already answered this question in a similar query I can easily adapt
for my use?
2. Is the information I need stored in the database in the format I need for my report?
3. Will the answer to my question require the use of more than one table?
4. Do I need to look for information in the database to eliminate everything but the answers
to the question I’m asking?
5. Is my logic for answering the question solid, and is there some way to verify the validity
of my answer?
Thinking systematically becomes a habit in problem-solving. Once applied to puzzles and
queries, this logic is easily applied to broader areas of life problems. Here’s an example of how
it might be applied to a big question, such as “Why am I here?”:
1. Has someone already worked on this question? What can I garner out of his/her
answers?
2. Is there a solid basis for determining what is/is not the meaning of life?
3. Is there anything I can safely eliminate from “meaningfulness”?
4. Is there anything that must be true in the final answer?