Sudoku color pairs
Posted by Dan on Mar 30th, 2008
2008
Mar 30
For sudokus in general, there are 46,656 ways to arrange the first color, and 17,972 ways to arrange the second color without overlapping the first color. 46,656 times 17,972 is 838,501,632, and adjust for double-counting, we get 419,250,816 possible patterns of two colors.
March 31st, 2008 at 5:03 am
HMMM.. I have been counting the number of 2 color pages put up between the full color sudoku and it seems to vary between 9 and 49 pages. I can’t seem to spot the duplicates. Are you playing with my head???
March 31st, 2008 at 9:37 am
The slide show program displays images at random, so the number of two-color pages displayed between the full-color page varies. The average should be 36, because that’s the number of two-color pages.
Sorry for the confusion. Maybe I can unrandomize the slide show.
March 31st, 2008 at 8:33 pm
I’m using WordPress, with a plug-in called NextGen Gallery, which uses a component called JW Image Rotator. It turns out that JW Image Rotator’s default behavior is to randomize the slide show, but there is a way to change this (set “shuffle” to “false”).
I think I learned something today.
April 1st, 2008 at 7:24 am
If one block of 9 - the upper right seems to be the systematic leader of the pack- was altered, by switching two cells and then allowing that to solve, how would that look? The dark blue and the maroon right underneath it, switch the blue from the upper right most corner down one row and put the maroon in the upper right most corner and have both puzzles bring up the same colors at the same time, just to see how the patterns change by one flutter of the butterfly’s wings. I like the pace of this one, although at first I thought it was too fast, but my eyes seem to be able to recognize the repeating patterns more quickly the more often I see it, but with two to look at, could you slow it down or put a speed controller on it?
Only in Nerdistan do I feel comfortable asking for such techie stuff. “Technological progress is like an axe in the hands of a pathological criminal.” -Albert Einstein….quoted from a new comic “ECHO” by Terry Moore.
April 1st, 2008 at 8:37 am
If you switch two cells in just one block, you break the sudoku pattern. So if you switch one block, you have to switch another block, and maybe another block after that. Switching one block results in a chain of blocks being switched, and the chains can be anywhere from 2 blocks long up to 9 blocks long, except for 8. (The proof that there are no chains of length 8 is left as an exercise for the reader.)
I can adjust the speed, but it may be difficult to do it without reloading the web page. I’ve thought about building an interactive sudoku viewer, with control buttons that you can click to do something to the sudoku, but there are so many possibilities that it’s hard to know where to start.
April 2nd, 2008 at 8:10 pm
If you change two blocks, in a pattern that will force the changing of the greatest number of additional blocks you could train college students to flip from one solved problem to the other and have one color at a time change across the board or grandstands. If I get 81 students I might try that. I have been thinking about chalking a sudoku grid and using different colored hats and see how fast people can rearranged themselves into a complex pattern.
CET
April 3rd, 2008 at 8:53 am
That’s a very interesting idea. I have thought about the nerdly version of it, namely writing a distributed sudoku solver, with 81 identical little sub-programs working together to solve the sudoku.
Sometimes this sort of thing is possible, sometimes it isn’t. Ants run simple programs, but the behavior of the whole colony is complex. Committees, on the other hand, seem to be stupider than individuals.
April 4th, 2008 at 5:46 am
Committees are as stupid as the main non-formal leader. Unfortunately, most committees are led by formal leaders who have reached their level of incompetence which includes barring non-formal leaders from participating.
I am thinking about how to form my people into blocks and keep it fun and I am thinking about a circular sudoku. It would be a circle in thirds, each third divided into thirds. I would put the 1st graders into the inner circle and as each grade student gets larger with longer arms, encircle each grade with students of the next grade up.
Remember the sudoku on the globe? If that were sliced in two or four, would it show the inside divided into colors and would those colors be in circles? Or was that only on the surface of the globe?