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 My not so fully analytical solution for difficult 8x8, 19-01 
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Posted on: Fri Jan 20, 2017 1:50 am




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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]


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




Posts: 2209
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:

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