View unanswered posts | View active topics It is currently Thu Mar 28, 2024 9:34 pm



← Back to the Calcudoku puzzle page




Reply to topic  [ 2 posts ] 
 My not so fully analytical solution for difficult 8x8, 19-01 
Author Message

Posted on: Fri Jan 20, 2017 1:50 am




Posts: 158
Joined: Sun Nov 03, 2013 10:28 pm
Post My not so fully analytical solution for difficult 8x8, 19-01
Since we only see real FAS'es on the forums, I thought some people might be interested to see how I sometimes use trial and error a lot to get to the right solution. This puzzle happens to be a perfect example; with a lot of fairly quick guesses I solved it in about 20 minutes. For reference, http://www.calcudoku.org/en/2017-01-19/8/3. So here we go:

1. Obvious stuff: pre-filled cells, [g1,g2]=[7,8], [c4,c5]=[5,6], [d8,e8]=[1,5], [f8,g8]=[2,8], [d3,d4] contains a 4.
2. f8=8, g8=2
3. [e5,f5]=[1,6] (the 3 and the 8 in the f column block the [3,8] possibility).
4. c4=6, c5=5
5. in g5, the only possible numbers left are 3 and 4. This means the [a5,b5] can't be [3,4], just [3,7] and [7,8], so [a5,b5] contains a 7.
6. GUESS: a8=4 and c8=7
6a. GUESS WITHIN A GUESS SORT OF: [c7,d7]=[2,6]. This gives c7=2, d7=6, [c2,c3]=[3,8], c6=4, but now there is no number that fits in d6. So [c7,d7] can't be [2,6].
6b. (Remove stuff from the previous guess) with the previous guess comes [c7,d7]=[3,5] (the [1,7] possibility is blocked because of the c column), so c7=3, d7=5.
6c. Only possible number in a7 is 1.
6d. Adding the first two columns gives that b1+b2+a5+b5=28. Using the the fact that [a5,b5] is [3,7] or [7,8], you'll see that you can't get this to work. This means the guess is wrong.
7. (remove stuff from the previous guess) with the previous guess comes a8=7 and c8=4.
8. b5=7, a5 is a 3 or an 8.
9. [c7,d7]=[3,8]. If c6=2, then [c2,c3] contains a 7 with which we can't get to 2 mod to work. so [c2,c3] contains a 2.
10. The only possibilities in a7 are 1 and 2.
11. Note that adding the first 2 columns gives b1+b2+a5+a7=19. Therefore, we
12. GUESS: a5=3
12a. Since 11., this gives a7=2 and [b1,b2]=[6,8], which then gives b1=8 and b2=6, which then gives g1=7 and g2=8.
12b. Trying the different possibilities in column b (or by calculating that a6-b3=2), we get b3=2, b7=a6=4 and b6=5.
12c. The 2 in row 1 has to be in h1. Also, g5=4 and h5=8.
12d. Now trying to fit the 4 somewhere in column h. Small hint: it won't work, so the guess is wrong.
13. (remove stuff from the previous guess) with the previous guess comes a5=8.
14. If a7=2, then b1+b2=9, which won't work. So a7=1. Then b1+b2=10, which gives [b1,b2]=[2,8] ([4,6] is blocked by row 1).
15. If b3=5, then [b6,b7]=[4,6] and a6=3, which is already blocked. So b3 is 4 or 6 and [b6,b7] contain a 5.
16. GUESS: b3=4
16a. Then [b6,b7]=[5,6], a6=2, d4=4, a2=4, [a3,a4]=[3,5].
16b. [e4,e5]=[5,7] ([3,5] gets blocked by a4), so a3=5 and a4=3.
16c. Try to fit a number in g4. Small hint, there's no number that fits in there, so the guess is wrong.
17. (remove stuff from the previous guess) with the previous guess comes b3=6.
18. b7=a6=4, b6=5, [a2,a3,a4]=[2,3,5]
19. if c6=7, then nothing fits in d6. So [c2,c3]=[2,7], c6=8, c7=3, d7=8.
20. Only number that fits in d6 is 6.
21. Only number that fits is g6 is 1
22. The 6 in column g only fits in g7.
23. [g3,g4]=[3,5], g5=4, h5=3, h3=1
24. f7 is a 5 or a 7. If f7=5, then [e6,e7]=[2,7] and [h6,h7]=[2,7] would give two solutions, which can't be the case. So f7=7.
25. The 8 in column h only fits in h4.
26. The 4 in column h only fits in h2, then h1=5, h7=2, h6=7, e6=2, e7=5
27. The 2 in row 1 only fits in b1.
After this is should be pretty straight forward.

Please don't yell at me for missing obvious clues [lol]


Profile
User avatar

Posted on: Fri Jan 20, 2017 9:38 am




Posts: 3296
Joined: Thu May 12, 2011 11:58 pm
Post Re: My not so fully analytical solution for difficult 8x8, 1
Thanks :)

Here's the puzzle for reference:

Image


Profile
Display posts from previous:  Sort by  
Reply to topic   [ 2 posts ] 

You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum

Search for:
Jump to:  
cron
All forum contents © Patrick Min, and by the post authors.

Forum software phpBB © 2000, 2002, 2005, 2007 phpBB Group.
Designed by STSoftware.