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Re: [Phys-l] tomography exercise

I've been doing the SuDoKu thing for a coupla years now and have spent some time wondering how the algorithm works that generates a 'successful' game board.
I've been given some excessively poorly done books that indeed show 'degeneracies' in the solution.
(JD's example below is four-fold degenerate?)
When a puzzle actually has a ZERO in one of the 'given' squares - I know that I have witnessed the ultimate in poor editing.

I've wondered how many possible completed boards are possible (discounting the degeneracies) but haven't yet finished that calculation. It reminds of the eight queens on the chess board problem and probably shares some of that puzzles properties.

Does this in fact relate to the CT image generation?
I ask because we are currently marveling over some CT headshots - wondering how an empty sinus up shows so clearly.

(The scattering from metal fillings is interesting too.)

At 6:00 AM -0700 3/15/10, John Denker wrote:
By way of background:
In NMR imaging aka computed tomography (CT), you don't
start out with an image. You have to compute the image,
pixel by pixel. Roughly speaking, the raw data might tell
you the sum of pixels for each rank and file and column
(i.e. summing in the X, Y, and Z directions, respectively)
and you have to compute the pixels from that.

The exercise for today is much simpler. Rather than using
the sums mentioned in the previous paragraph, we are just
going to use Su Doku rules. That is, each digit 1 through
9 must appear once in every row, once in every column, and
once in every 3x3 cell.

You should be able to solve this Su Doku instance very quickly.
A "hard" puzzle might have only 17 or 18 givens, but this one
has 73 givens. Most of the work has already been done.

5 4 8 | 6 7 1 | . 3 .
. . 2 | 3 4 5 | 1 6 8
1 3 6 | 9 8 2 | 7 5 4
-------+-------+-------
3 5 7 | 4 1 6 | . 8 .
4 2 1 | 8 5 9 | 6 7 3
8 6 9 | 2 3 7 | 5 4 1
-------+-------+-------
6 1 4 | 7 9 3 | 8 2 5
2 8 5 | 1 6 4 | 3 9 7
. . 3 | 5 2 8 | 4 1 6

So, what is your answer to this puzzle? Imagine that this
is a medical imaging situation, and we need a reliable answer
right away.

And ... how sure are you of the answer? This is important,
because the patient's life hangs in the balance.
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