Strange things in 2x2 sudoku's

soduko · Posted: Mon Oct 31, 2005 1:04 am Post subject: Strange things in 2x2 sudoku's

while I was browsing the forum I came to the thread
http://www.setbb.com/phpbb/viewtopic.php?t=27&mforum=sudoku

And made a simplistic BASIC program to make all 288 2x2 sudoku's

In my simplistic program I made 8 nested loops from 1 to 4 for the variables
R1C1, R1C2, R1C3, R2C1, R2C3, R3C1, R3C2 and R3C3

the other variables were calculated from these loopvariables like:
R1C4 = 10 - R1C1 - R1C2 - R1C3
and
R2C2 = 10 - R1C1 - R1C2 - R2C1

And then did all the testing
- not two the same values in a row, column and box

There are 6 (tests per row, column and box)
times
8 (number of rows and collumns)
plus
2 (extra tests per box, the other 4 are already in the row and column tests)
times
4 (number of boxes)

total 56 tests. (corrected original gave 54 by mistake)

By mistake I forgot some tests but strangly (to me) this did not result is extra (wrong) solutions.

Some puzzeling later I found that I only had to do

the following 19 tests:

R1C2 = R1C1
R1C3 = R1C1
R1C3 = R1C2
R2C1 = R1C1
R2C1 = R1C2
R2C3 = R1C3
R2C3 = R2C1
R2C3 = R2C2
R3C1 = R1C1
R3C1 = R2C1
R3C2 = R1C2
R3C2 = R3C1
R3C2 = R2C2
R3C3 = R1C3
R3C3 = R2C3
R3C3 = R3C1
R3C3 = R3C2
R4C3 = R4C1
R4C3 = R4C2

Can somebody explain this to me?
I noticed that only the last two tests involve calculated variables, but I do not understand why, they are nessesary and the others are not.

Ps I do not understand DLX and QWH's
And Graph theory is also still uncharted.