Tough Sudoku for 18/March/2006

17:08 easy tough today for a change!

10:28

But if x-wing link h3,b6 forbids c4=6 we see I2=1 or b7=5 so in any case I1=2 is forbidden, allowing the weakly linked 3's to confirm s2 is locked. Knowing that, we can see that neither g1,I1=4 leading to E1=4, consequently easy to 81. Its a no-brainer, really. Happy St. Pat's day!

Steve: I am afraid your ingenious depth 11 solution of yesterday's puzzle needs a more complicated matrix pattern than the one I described above. Bruno and I have those too but they are too complicated to explain here.

DJ: I am not sure what you mean by 'color.' Our statement is this: if there is a square matrix whose entries are sets of candidates (possibly empty) so that the union in each row is a strong set, and in every column but one each pair of entries is in conflict, then the union of entries in the remaining column is a strong set. To see this, argue by contradiction and use Pigeonhole Principle.

Exactly what puzzle is Mensa Man talking about?

Andrei: I meant numbers or atoms. I wasn't able immediately to relate your example to the POU theorem. I think I get it now.

The pigeonhole theorem is exactly what the 'Almost Locked Sets' idea uses, every single time. The generalization of same requires either a contradictory proof, or one could easily construct a proof by induction after showing validity on a trivial set. I think so, anyway.

Could anyone tell me how you guys approach to these puzzles using matrices.I dont use no particular strategy to solve,I guess, I have completed it in a crude way.

Wish I could figure out your 'code' for solving, because it seems like so much Greek to me! I'm not a Mensa member or even close! But I sure enjoy solving, even with check moves. And I enjoy the descussions about ways to solve.

21:46 Good mAen all!

19.33 i got to 46 filled and then looked at some of the solutions to help me get 'unstuck' it seems so easy when you have the solution there...but i am starting to get the toughs sometimes...many thanks to all the sudokers who have assisted me in the past week.
also, for the uninitiated, the rows are numbered 1 to 9 starting from the bottom and columns are listed as a to i starting from the left. so a1 is the most bottomleft corner of the grid and i9 is the topright corner

I'm with Karen from NR OH - Steve and the gang - what are you all talking about???

Happy Paddy's Day to my favourite geeks!!!

De\r Steve & Andrei I love reading your posts...unfortunatly they make no sense to me what so ever....needless to say I am no where near solving the puzzle....will have to look on a site for 'idiots guide'....back to my comfort zone mediun/hard!! cheers all!

24:29 - I actually think I solved this one without using x-wing or y-wing or any of those techniques that I'm just beginning to understand. Is that possible, or did I just make a lucky mistake?

Either today's tough was easier than usual or I'm getting better at this.

7.54 thought that was straight forward and quite easy for a toughie
who are the cheeky pair in the picture
have a great day/night one and all
Happy St Patricks day to those still on the 17th

easy...'touching' picture

16:10 cute boys

17:49 after setup. Much better than yesterday's tough!

ok

10:54

July 2, 2007.

SE=4.5

14:56.