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| Armageddon
| | Joined: 16 Mar 2006 | | Posts: 2 | | : | |
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 Posted: Thu Mar 16, 2006 6:34 pm Post subject: Sudoku diagonal??? |
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hi, i have a problem...
this sudoku must be solved with the numbers in the diagonal 1-9,too.
i tried it many times but cant find a solution...
plz help |
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| Ruud
Site Admin
 | | Joined: 17 Sep 2005 | | Posts: 708 | | : | | Location: Netherlands |
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| Posted: Thu Mar 16, 2006 7:38 pm Post subject: |
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Hi,
how far did you get?
When you are stuck in a sudoku, it is a good idea to ask other people to help you, but we can help you better if we know where you are stuck.
I will tell you how to solve this puzzle completely, but do not scroll down and read the last chapter!
The first 2 digits can be placed without any trouble:
| Code: | .------------------------.------------------------.------------------------.
| 1567 156789 2 | 18 18 3 | 4 1678 16 |
| 167 1678 3 | 4 2 9 | 5 1678 16 |
| 4 18 18 | 5 7 6 | 23 1238 9 |
:------------------------+------------------------+------------------------:
| 9 124567 1457 | 1367 1456 2457 | 2367 123567 8 |
| 12567 1245678 14578 | 13678 145689 2457 | 23679 1235679 12356 |
| 3 125678 1578 | 1678 15689 257 | 2679 125679 4 |
:------------------------+------------------------+------------------------:
| 8 45 45 | 2 3 1 | 69 4569 7 |
| 257 23457 6 | 9 45 8 | 1 2345 235 |
| 1257 123457 9 | 67 456 457 | 8 23456 2356 |
'------------------------'------------------------'------------------------' |
Please note the pair of {1,8} in row 1, confined to 2 cells, and a similar pair in row 3. There is also a pair {4,5} in row 7. These lead to the following eliminations and placements:
| Code: | .------------------------.------------------------.------------------------.
| 5 9 2 | 18 18 3 | 4 7 6 |
| 67 67 3 | 4 2 9 | 5 8 1 |
| 4 18 18 | 5 7 6 | 23 23 9 |
:------------------------+------------------------+------------------------:
| 9 124567 1457 | 1367 1456 2457 | 2367 12356 8 |
| 1267 1245678 14578 | 13678 145689 2457 | 23679 123569 235 |
| 3 125678 1578 | 1678 15689 257 | 2679 12569 4 |
:------------------------+------------------------+------------------------:
| 8 45 45 | 2 3 1 | 69 69 7 |
| 27 237 6 | 9 45 8 | 1 2345 235 |
| 127 1237 9 | 67 456 457 | 8 2345 235 |
'------------------------'------------------------'------------------------' |
At this point, we need to use the diagonals. Eliminate all candidates in the diagonal cells that are already present in those diagonals.
This leads us here:
| Code: | .------------------------.------------------------.------------------------.
| 5 9 2 | 18 18 3 | 4 7 6 |
| 67 67 3 | 4 2 9 | 5 8 1 |
| 4 18 18 | 5 7 6 | 23 23 9 |
:------------------------+------------------------+------------------------:
| 9 124567 1457 | 1367 1456 2457 | 2367 12356 8 |
| 1267 1245678 14578 | 13678 149 2457 | 23679 123569 235 |
| 3 125678 1578 | 17 15689 27 | 2679 12569 4 |
:------------------------+------------------------+------------------------:
| 8 45 45 | 2 3 1 | 69 69 7 |
| 27 237 6 | 9 45 8 | 1 234 235 |
| 127 1237 9 | 67 456 457 | 8 2345 23 |
'------------------------'------------------------'------------------------' |
Now there is only a single candidate for digit 8 in the diagonal that runs from top-left to right-bottom. Because it is one of a pair, the other cell in that pair can also be placed:
| Code: | .---------------------.---------------------.---------------------.
| 5 9 2 | 18 18 3 | 4 7 6 |
| 67 67 3 | 4 2 9 | 5 8 1 |
| 4 1 8 | 5 7 6 | 23 23 9 |
:---------------------+---------------------+---------------------:
| 9 24567 1457 | 1367 1456 2457 | 2367 12356 8 |
| 1267 245678 1457 | 13678 149 2457 | 23679 123569 235 |
| 3 25678 157 | 17 15689 27 | 2679 12569 4 |
:---------------------+---------------------+---------------------:
| 8 45 45 | 2 3 1 | 69 69 7 |
| 27 237 6 | 9 45 8 | 1 234 235 |
| 127 237 9 | 67 456 457 | 8 2345 23 |
'---------------------'---------------------'---------------------' |
Box 7 has a single candidate for 1 in r9c1.
Eliminate 1 from the remainder of that diagonal to reveal a naked 7.
This forces a 2 in r6c6. Clear the diagonal of 2 to reveal a naked 3 in r9c9.
From then on, the puzzle can be solved a long way with singles only, upto this point:
| Code: | .---------------.---------------.---------------.
| 5 9 2 | 18 18 3 | 4 7 6 |
| 6 7 3 | 4 2 9 | 5 8 1 |
| 4 1 8 | 5 7 6 | 23 23 9 |
:---------------+---------------+---------------:
| 9 46 147 | 13 16 5 | 2367 1236 8 |
| 2 68 17 | 138 19 4 | 3679 1369 5 |
| 3 568 15 | 7 1689 2 | 69 169 4 |
:---------------+---------------+---------------:
| 8 45 45 | 2 3 1 | 69 69 7 |
| 7 3 6 | 9 5 8 | 1 4 2 |
| 1 2 9 | 6 4 7 | 8 5 3 |
'---------------'---------------'---------------' |
A 3 in r4c4 can be eliminated due to the diagonal, leaving a single 1.
A few rounds of singles brings you to the final decision:
| Code: | .---------.---------.---------.
| 5 9 2 | 8 1 3 | 4 7 6 |
| 6 7 3 | 4 2 9 | 5 8 1 |
| 4 1 8 | 5 7 6 | 23 23 9 |
:---------+---------+---------:
| 9 4 7 | 1 6 5 | 23 23 8 |
| 2 8 1 | 3 9 4 | 7 6 5 |
| 3 6 5 | 7 8 2 | 9 1 4 |
:---------+---------+---------:
| 8 5 4 | 2 3 1 | 6 9 7 |
| 7 3 6 | 9 5 8 | 1 4 2 |
| 1 2 9 | 6 4 7 | 8 5 3 |
'---------'---------'---------' |
Now check the diagonal to see what goes where.
Ruud.
_________________
Meet me at sudocue.net |
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| elroy
| | Joined: 16 Mar 2006 | | Posts: 6 | | : | |
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| Posted: Thu Mar 16, 2006 7:52 pm Post subject: |
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Not sure I understand -- If its a valid Sudoku (with but one unique solution) the diagonals would fall in automatically without regarding them, so are the diagonals an additonal clue to HELP solve it? -- otherwise, accepting them as an additional rule simply seems to complicate the normal logical Soduko processes unnecessarily..
But I'm no expert
elroy
[edit] Looks like this was premature - Raud came in (above) at same time I was submitting.
Last edited by elroy on Thu Mar 16, 2006 7:59 pm; edited 1 time in total |
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| Armageddon
| | Joined: 16 Mar 2006 | | Posts: 2 | | : | |
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| Posted: Thu Mar 16, 2006 7:59 pm Post subject: |
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wow thx...
i've found my faults...but i wasn't wrong at all i had just one logical mistake..
thank you
| Quote: | Not sure I understand -- If its a valid Sudoku (with but one unique solution) the diagonals would fall in automatically without regarding them, so are the diagonals an additonal clue to HELP solve it? -- otherwise, accepting them as an additional rule simply seems to complicate the normal logical Soduko processes unnecessarily..
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i thought so, too |
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| m_b_metcalf
| | Joined: 13 Mar 2006 | | Posts: 210 | | : | | Location: Berlin |
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| Posted: Thu Mar 16, 2006 8:30 pm Post subject: |
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| elroy wrote: | Not sure I understand -- If its a valid Sudoku (with but one unique solution) the diagonals would fall in automatically without regarding them, so are the diagonals an additonal clue to HELP solve it? -- otherwise, accepting them as an additional rule simply seems to complicate the normal logical Soduko processes unnecessarily..
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Yes, and it's called an X-sudoku. Christoher Monckton has published a book of them. The additional constraint is not necessarily a help in finding a solution. It is usually used to reduce the number of givens and hence to increase the difficulty of finding the solution. I have generated some that have only 15 givens (note that rows 2 and 6 and column 3 are empty):
| Code: |
8
6 4 9
4 8 1
3 5
3 7
6 9 5
4
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Regards,
Mike Metcalf |
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| Guepardo
| | Joined: 14 Jan 2007 | | Posts: 5 | | : | |
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| Posted: Mon Jan 15, 2007 2:48 pm Post subject: |
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| Yeah! It's very clear now, good explication! |
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| Nathan
| | Joined: 22 Jan 2008 | | Posts: 6 | | : | |
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| Posted: Tue Jan 22, 2008 10:42 am Post subject: |
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| huh? |
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