a partial sudoku puzzle

MattcAnderson · 2017-06-28, 14:43

Hi MersenneForum,

I picked up a Sudoku book today and tried again at a puzzle that had stumped me before. I was able to put in the number 8 near the center and then I was again stumped.

I know there are some advanced Sudoku techniques out there, on the internet. Can anyone tell me a next step ( with logic) for the attached puzzle?

Also the possibility of a machine solver has been considered. This is from the "New York Post Bloom Sudoku Book" (fiendish puzzles c 2013). I am stuck on page 31.

I do not want to 'reverse engineer' the puzzle by looking in the answer section.

Regards,
Matt

CRGreathouse · 2017-06-28, 15:14

Well, in the top-right box you can fill in a 6 (in the bottom-middle position) because nothing else in the middle column can be a 6. Similarly the middle row across the top has only one position to put a 9, the middle of the left grid. That forces the "49" at the bottom to 4 and the "47" above it to 7, and probably cascades further.

science_man_88 · 2017-06-28, 21:14

Quote:

Originally Posted by MattcAnderson

Hi MersenneForum,

I picked up a Sudoku book today and tried again at a puzzle that had stumped me before. I was able to put in the number 8 near the center and then I was again stumped.

I know there are some advanced Sudoku techniques out there, on the internet. Can anyone tell me a next step ( with logic) for the attached puzzle?

Also the possibility of a machine solver has been considered. This is from the "New York Post Bloom Sudoku Book" (fiendish puzzles c 2013). I am stuck on page 31.

I do not want to 'reverse engineer' the puzzle by looking in the answer section.

Regards,
Matt

Lets rewrite it here, on the forum ( in roughly,original form), instead of the file and rotating it:

$ \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline &&6&&&&&9\\ \hline &&2&8&&6&&&1\\ \hline 8&1&&&5&&&&\\ \hline &5&&&2&&&&\\ \hline &&3&7&6&1&9&&\\ \hline &8&&&3&&&1&\\ \hline &&&&9&&&4&3\\ \hline &&&3&&7&6&&\\ \hline 2&&&&&&1&&\\ \hline \end{tabular}$

now it's mostly a combination of set union, and set difference to consider.

chalsall · 2017-06-28, 21:36

Quote:

Originally Posted by science_man_88

...now it's mostly a combination of set union, and set difference to consider.

Indeed. This puzzle is trivial to solve.

"2" is the only possible solution for 2x,5y. Everything simply cascades.

MattcAnderson · 2017-06-29, 07:14

Hi Mersenne Forum,

Thank you to all the responses to this thread.
I see Greathouse's reasoning for a 6 in the bottom row of the top right 3 by 3 grid.

Now this one should be easy.

Regards,
Matt

2017-06-29, 07:14	#5
MattcAnderson "Matthew Anderson" Dec 2010 Oregon, USA 2³×149 Posts	thanks Hi Mersenne Forum, Thank you to all the responses to this thread. I see Greathouse's reasoning for a 6 in the bottom row of the top right 3 by 3 grid. Now this one should be easy. Regards, Matt

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2017-06-28, 15:14	#2
CRGreathouse Aug 2006 1011101100100₂ Posts	Well, in the top-right box you can fill in a 6 (in the bottom-middle position) because nothing else in the middle column can be a 6. Similarly the middle row across the top has only one position to put a 9, the middle of the left grid. That forces the "49" at the bottom to 4 and the "47" above it to 7, and probably cascades further.