## Finishing Off

Post the puzzle or solving technique that's causing you trouble and someone will help

### Finishing Off

Occasionally I find that I get stumped with a puzzle right near the end, where the remaining numbers to complete it are largely part of an extended bi-value chain. Always wanting a result, I naturally fall back on brute force with the mighty pen (never a computer). With only two possible options, one of them has to be right, but I always feel I should be able to just see straight away what will work and what will not. Here's a couple of examples:
067351024103820765205706013310472506724605130056130247400513672672900351531267400
073800125281035604504021380325408710710350248408172503030287451157000832842513900
Both these have about 20 numbers to go. The first has a chain of mainly 8s or 9s, but is r1c1 8 or 9? I searched every way I knew but could not see that either of these was excluded by any of the available variables. Similarly, the 2nd example has mostly options of 6 or 9. Has anyone got a quick-scan technique that would easily disprove one of them?
Yogi
2017 Supporter

Posts: 124
Joined: 05 December 2015
Location: New Zealand

### Re: Finishing Off

Code: Select all
`+----------------+-------------+------------+| 8-9   6     7  | 3  5   1    | 89  2   4  || 1     4(9)  3  | 8  2   4(9) | 7   6   5  || 2     489   5  | 7  49  6    | 89  1   3  |+----------------+-------------+------------+| 3     1     89 | 4  7   2    | 5   89  6  || 7     2     4  | 6  89  5    | 1   3   89 || 8(9)  5     6  | 1  3   8(9) | 2   4   7  |+----------------+-------------+------------+| 4     89    89 | 5  1   3    | 6   7   2  || 6     7     2  | 9  48  48   | 3   5   1  || 5     3     1  | 2  6   7    | 4   89  89 |+----------------+-------------+------------+`
Skyscraper : {9R26} -> -9r1c1; stte
Code: Select all
`+--------------+---------------+--------------+| 69  7     3  | 8    469  469 | 1  2    5    || 2   8     1  | 79   3    5   | 6  79   4    || 5   6(9)  4  | 679  2    1   | 3  8    7(9) |+--------------+---------------+--------------+| 3   2     5  | 4    69   8   | 7  1    6(9) || 7   1     69 | 3    5    69  | 2  4    8    || 4   6(9)  8  | 1    7    2   | 5  6-9  3    |+--------------+---------------+--------------+| 69  3     69 | 2    8    7   | 4  5    1    || 1   5     7  | 69   469  469 | 8  3    2    || 8   4     2  | 5    1    3   | 9  67   67   |+--------------+---------------+--------------+`
Skyscraper : {9C29} -> -9r6c8; stte
JC Van Hay

Posts: 719
Joined: 22 May 2010

### Re: Finishing Off

Yogi wrote:Has anyone got a quick-scan technique that would easily disprove one of them?

i used to select as shown below.
Code: Select all
`*-----------------------------*|-9       |    9  9 |         ||         | 9       |   *9    ||   *9    |-9       |      -9 ||---------+---------+---------||         |    9    |       9 ||      *9 |       9 |         ||   -9    |         |   -9    ||---------+---------+---------|| 9    -9 |         |         ||         | 9  9  9 |         ||         |         | 9       |*-----------------------------*`

if r3c2 = 9, r1c1, r3c49 and r6c2 > -9 then r2c8 and r5c3 = 9
This results r6c8 and r7c3 > -9. So, r6 lost possible candidates of 9
9r1c1 is correct because 9r3c2 > -9r6c28 = contradiction
is this quick-scan or not ?
Kozo Kataya

Posts: 33
Joined: 06 July 2012

### Re: Finishing Off

Alternatively for the first, all the unsolved cells have 2 candidates except one which has three. This allows you to apply the BUG+1 technique. This is described on many sudoku websites, the following is a good one: http://hodoku.sourceforge.net/en/techniques.php

Phil
pjb
2014 Supporter

Posts: 2025
Joined: 11 September 2011
Location: Sydney, Australia

### Re: Finishing Off

Thanx for the input guys. I was out of my depth with the other techniques but JC's Skyscrapers were magic. Now let's see if I've actually got it!
I take it that {9R26} means the skyscraper encompassing the 9-candidate cells in Rows 2 and 6, and -9r1c1 means r1c1 can't be a 9 because it can see both of the 9-candidate cells in the sloping end of the side-lying skyscraper, and one of those must be a 9. With r1c1 now fixed at 8 the puzzle is solved. I suppose the right lingo is 8r1c1 or r1c1 -> 8
The 2nd case is equally simple once spotted. With {9C29} we have the upside-down skyscraper drawn by the 9-candidate cells in Columns 2 and 9. This eliminates 9 from r6c8 which can see both cells in the sloping edge of the skyscraper. Now, with the values in r6c2 and 8 fixed this puzzle is also quickly solved.
I'm not sure what stte means. Maybe it's short for SORTED!
One general observation I drew from all this is that the first puzzle had only candidates 4, 8 and 9 to play with and the second had only 6, 7 and 9 (4 was not important) which made looking for skyscrapers a lot easier.

Regards!
Yogi
2017 Supporter

Posts: 124
Joined: 05 December 2015
Location: New Zealand

### Re: Finishing Off

"stte" means Singles To The End.

Which means nearly the same thing as Sorted

JasonLion
2017 Supporter

Posts: 640
Joined: 25 October 2007
Location: Silver Spring, MD, USA

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