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May 16 puzzle surprise

 
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tran
New kid on the Grid
New kid on the Grid


Joined: 27 May 2006
Posts: 1

PostPosted: Sat May 27, 2006 8:20 pm    Post subject: May 16 puzzle surprise Reply with quote

I just found this site last week and have been doing the recent daily nightmares and found the May 16 very surprising. Let me explain how I solve these puzzles and why this one is amazing. I fill out the puzzle as much as I can using simple logic (e.g. cross hatching) which usually is about 5 cells for the nightmares. I don't use any advanced techniques that I have seen discussed here at all since I don't mark every cell with possible candidates. I only look at the cells with 2 possible candidates. What I do next is to use the bifurcation technique. I look for a cell with 2 candidates or a candidate that can only go in two cells of a house. I pick one and follow as far as I can until I find an inconsistency and back track. This is not efficient if one encounters many forks before an inconsistency is found. So I try to find a starting point that will get me as many cells as possible that way I will likely encounter an inconsistency in very few forks.
Luckily the nightmares seem to have this characteristics. This is the surprise of the May 16 nightmare. The first guess leads me to an inconsistency without needing another fork. But the biggest surprise is that the other choice (actual it is not a two but three prong fork that I chose) complete the solution without another guess being required.

Let me show what I mean. From the start I can only get 4 additional cells: (2,4), (6,4), (9,5) and (7,6). Here is what it looks like

2 0 0|8 0 3|0 0 0
1 3 0|9 0 2|0 0 6
0 0 9|0 5 0|0 0 0

0 2 0|0 0 0|7 0 0
0 4 0|7 0 1|0 3 0
0 0 6|0 0 0|0 5 0

0 0 0|0 2 7|8 0 0
8 0 0|4 0 0|0 7 9
0 0 0|3 8 9|0 0 1

In box 2 the missing 6 can go in (1,5), (3,4) or (3,6). My first choice was (3,6) that took me to an inconsistency without another guess. My next guess was (3,4) and that solve the whole puzzle without another fork!!!

So the puzzle was done in 10 minutes.

Did anybody find this?

Was this an accident?
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Ruud
Site Owner
Site Owner


Joined: 30 Dec 2005
Posts: 601

PostPosted: Sun May 28, 2006 12:40 am    Post subject: Reply with quote

Hi Tran, welcome aboard!

Every sudoku has multiple backdoors. Even the toughest puzzles from my collection have 15 backdoors or more. A backdoor is a cell that, when you guess its value correctly, the puzzle is solved with basic techniques.

All the Daily Nightmares can be solved without guessing. If you choose not to guess, you are faced with challenging puzzles that require an interesting mix of solving techniques. One of the criteria for my nightmares is a limit to the number of singles to start with. Another is a minimum number of advanced steps and variation in techniques.

If you choose to guess, these puzzles lose a lot of their appeal. But that's just my advice. Solve the puzzles anyway you like, as long as you enjoy them.

cheers,
Ruud.
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