Mark asked:


i am stuck on this and i refuse to be beaten by a piece of paper. i am doing easy puzzle 4 of volume 25. any tips or help at all? it is a math based game where there are 9 boxes of 9 squares each. there are predetermined numbers in the puzzle. each box must have 1 of all numbers from 1-9. and the numbers cannot match vertically or horizontally. help me please.

Brasshopper asked:


I apologize for this but I do not have way to set fixed fonts or colors, or I would have set the below up and then colored the puzzle as far as I could. I also can’t attach a file or I would have attached the simple sudoku file that represents this puzzle. The groups with X’s in them are repeats of the groups above them where I attempt to use X’s to make up for the proportional font problems.

Puzzle as presented:

*———–*
|5..|.83|7..|
|1.3|.9.|4..|
|7..|..5|3..|
|—+—+—|
|4.5|7..|…|
|…|.4.|…|
|…|..8|5.1|
|—+—+—|
|..1|8..|..4|
|..6|.7.|1.9|
|..9|15.|..7|
*———–*

|5xx|x83|7xx|
|1×3|x9x|4xx|
|7xx|xx5|3xx|
|—+—+—|
|4×5|7xx|xxx|
|xxx|x4x|xxx|
|xxx|xx8|5×1|
|—+—+—|
|xx1|8xx|xx4|
|xx6|x7x|1×9|
|xx9|15x|xx7|
*———–*

This was how far I’d worked it out when I tried to color 2′s:

*———–*
|59.|.83|71.|
|1.3|297|4.5|
|7..|.15|39.|
|—+—+—|
|4.5|7..|9..|
|9..|54.|.7.|
|6.7|9.8|541|
|—+—+—|
|371|8.9|.54|
|.56|374|1.9|
|.49|15.|.37|
*———–*
*xxxxxxxxx*
|59x|x83|71x|
|1×3|297|4×5|
|7xx|x15|39x|
|xxx+xx+xxx|
|4×5|7xx|9xx|
|9xx|54x|x7x|
|6×7|9×8|541|
|xxx+xx+xxx|
|371|8×9|x54|
|x56|374|1×9|
|x49|15x|x37|
*xxxxxxxxx*

This was the puzzle as I was working on it. Single numbers are set and should match the last array, while any multiple numbers are pencil marks as I’ve computed them.
*————————————————–*
| 5 9 24 | 46 8 3 | 7 1 26 |
| 1 68 3 | 2 9 7 | 4 68 5 |
| 7 268 248 | 46 1 5 | 3 9 28 |
|—————-+—————-+—————-|
| 4 138 5 | 7 36 12 | 9 268 38 |
| 9 13 28 | 5 4 16 | 28 7 36 |
| 6 23 7 | 9 23 8 | 5 4 1 |
|—————-+—————-+—————-|
| 3 7 1 | 8 26 9 | 26 5 4 |
| 28 5 6 | 3 7 4 | 1 28 9 |
| 28 4 9 | 1 5 26 | 68 3 7 |
*————————————————–*

I’m part way through solving the above puzzle. Frame 1 is the initial layout, frame 2 is what I’ve worked out so far, and frame 3 includes pencil marks whenever you see multiple marks in a square.

Coloring is a technique where you try to eliminate candidates by making the candidates into a chain of pairs. There are two possibilities. One is that you will be able to put two cells of the same color into a set, meaning that that candidate exists in the other color – which is the sort of discovery that collapses a hard puzzle into an easy one. The other is that there will be cells that can see both colors and therefore can be eliminated as candidates themselves. The rule is that you find a pair (two candidates, and only two candidates that are in the same set). When one of those candidates can see one of another pair, then that pair can be added to the chain. You start pretty much anywhere and add pairs as they are visible. I’ve eliminated several candidate 2′s bases on the 2,8 pair in row 5 and the pointer in column 9, and I’m trying to color out the rest.

So I try to color 2′s. I do the usual thing of finding some conjugate pairs that can see other conjugate pairs. The pair I mention can see the next pair I add. Thus I start in the lower left corner and work my way through the puzzle.

R8C1 -> pink, R7C1 -> blue.
R8C6 ->blue, R7C5 is pink.
R7C7 -> pink, R8C8 -> blue.
R4C7 ->blue, R5C6 -> pink.
R6C5 -> blue, R4C6 -> pink.
R6C2 -> pink, R5C3 -> blue.
R3C2 -> blue.

Now is where I have the problem. I believe I can see a pair at R3C9, (red), R1C9 (Blue) from R3C2. Or I can see a pair from R5C3 at R1C3, R1C9 (pink, blue).

Either of these observations shows R3C3 as being able to see cells of opposite colors, which SHOULD allow me to clear the candidate 2 from R3C3.

Except that the 2 is at R3C3 and it can then see 2′s of opposite colors. I just do not get it.

Does anyone know what I did wrong? I have looked at the explanations of coloring at, say, http://www.sudopedia.org/wiki/Simple_Colors and I think I’m doing it right. But it is obviously not working so I guess I don’t get it.
I made a couple of typos when I described my coloring chain. It should be R8C1 and R9C1 as your first pair.
Then R9C6 and R7C5.
Then R7C7, R8C8.
Then R4C8, R5C7.
Then R6C5, R4C6.
Then R6C2, R5C3.
Finally R3C3 ends the last conjugate from R5C3.

I made like 4 typos in that list, and I thought I’d double checked it, sorry.

When I wrote this question, it had color coding in it because the interface I was able to use allowed for more general editing.

But the remaining parts of the question, am I right in coloring the R1C3-9 or C9R1-3 conjugate pairs to match the existing pairs I’ve marked? Obviously not, since it leads to the wrong answer. But when I read the rules on coloring pairs, I think I’m supposed to mark them, and I’m trying to figure out what I’m missing.