Cool Clock Confluences

No mathematical activity is more fun than when numbers seem to line up in a mystical way. Watching a car's odometer turn over from 299,999.9 miles to 300,000 miles is a major numeric event.

So it was that on June 6, 2006 (ummm... that's 6/6/06 in case you weren't paying attention) I noticed several significant times of the day:

1:11
2:22
3:33
4:44
5:55
and last, but not least, the longest one: 11:11.

I wasn't around for both the AM and PM version of these, but that does double the list.

What does this all mean?

Not a thing that I can see, but it is sort of cool to watch these times appear on a digital clock and stare at them for 59 seconds until your eyes water and they pass into eternity.

Summer Dot: Sudoku System

Having watched dozens of friends and acquaintances scribbling gazillions of jumbled numbers all over their Sudoku puzzles, I've decided to reveal my hitherto "secret" Summer Dot Sudoku system.

I haven't figured out how to either make or post a diagram, so you'll have to use your imagination a little bit, but it's not hard.

What is this all about?

It's a simple, neat way to keep track of which number could/should go in each empty Sudoku square without writing numbers all over the place: It uses dots instead.

First, draw an empty 3 x 3 square with 9 empty boxes. It should look just like any of the 9 square units that make up a 9x9 Sudoku puzzles.

For reference, fill the squares with numbers from 1 to 9
Minus the lines, it will look something like this:

1 2 3
4 5 6
7 8 9

Now draw another empty 3 x 3 square. Imagine that the _ is really an enclosed box

_ _ _
_ _ _
_ _ _

Suppose you want to represent the number 5 with a DOT instead of the number 5. Where would you put it?
Did you answer "the middle square?" Yep!

_ _ _
_ * _
_ _ _

How about 8?

_ _ _
_ _ _
_ * _

So any number can be represented by a DOT (represented by *) in the appropriate square.

Instead of trying to write down all the actual numbers that can go into a square, just put a DOT in the appropriate spot within the empty square. This works best with large Sudoku puzzles with large squares or with a very fine point pen that lets you make little tiny dots.

It takes a little practice to become accustomed to reading the dots as numbers:

*_ _
_ _ _
_ _ _

= 1

_ * _
_ _ _
_ _ _

= 2

and so on.

Patterns of missing numbers emerge very quickly.

If a given square can hold 1, 5, 7, 8 it would look like:

* _ _
_ * _
* * _

with the four dots in the appropriate spaces.


2, 6, 8, 9 would look like:

_ * _
_ _ *
_ * *

As you fill in other squares and use up a "missing" number, simply erase the DOT (if you are using pencil) or draw a thin line through it if you are brave and do Sudoku with a pen.

Any questions?

Happy solving!