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Killer Sudoku solving strategies http://www.calcudoku.org/forum/viewtopic.php?f=19&t=756 
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Author:  pnm [ Sun Dec 06, 2015 10:02 pm ] 
Post subject:  Killer Sudoku solving strategies 
Someone wrote to me that puzzle 126 of the new "Colossal Killer Sudoku" book was especially difficult. I started solving it, and got a start in it pretty quickly. I'll describe the steps below, and am inviting other puzzlers to add suggestions Here's the puzzle: Some initial steps:  the sum of all cages in columns a, b, c, and d = 184, so e4 = 4  the sum of all cages in rows 1, 2, and 3 = 146, so a4 + h4 = 11: doesn't help me much, other than determine that a4 cannot be 1  using similar steps, d6 + f6 = 12 (doesn't help me yet)  the "17" cage at d8d9 must hold 8 and 9  so the "11" cage at e7e8 must hold 5 and 6  so the "17" cage at e1e2e3 must hold 1, 7, and 9  so e5e6 must have 3 and 8, so f5 = 1  so e9 = 2 and f9 = 3 After these steps (more or less): 
Author:  pnm [ Sat Dec 12, 2015 5:19 pm ] 
Post subject:  Re: Killer Sudoku solving strategies 
Some further steps:  from the numbers in the centre 3x3 box we see that d4d5 have to hold 2 and 6 (in some order)  so f4 = 9  so f1f2f3 have to hold 2,6,8 (in some order)  so d1d2d3 have to hold 3,4,5 (in some order)  so d1 = 5 (otherwise we can't make 8 in the cage c3d2d3)  so c3 = 1  so b2b3 hold 2,5 (in some order)(not 3,4 because then the puzzle solution would no longer be unique)  the cages in the top left add up to: 19 + 16 + 7 + 8 + 10 = 60 extending from there are d1d2d3 and a4. The sum of the numbers in d1d2d3: 12 so a4 = 60  45  12 = 3  so a3 = 7  from adding all cages in the top 3 boxes and a4 and h4 we find that h4 = 8  so h3 + i3 = 8, so they hold 2,6 or 3,5  so i1i2 holds 1,4 (and not 2,3) The situation after these steps: 
Author:  nailhouse [ Sun Dec 13, 2015 11:37 pm ] 
Post subject:  Re: Killer Sudoku solving strategies 
pnm wrote: ...because then the puzzle solution would no longer be unique... 
Author:  nicow [ Mon Dec 14, 2015 11:42 am ] 
Post subject:  Re: Killer Sudoku solving strategies 
nailhouse wrote: pnm wrote: ...because then the puzzle solution would no longer be unique... This is a fundamental strategy for sudoku, called 'unique rectangles'. At this moment d2d3 holds {3,4} so, if b2b3 also should hold {3,4} two solutions would be found, because the four cells form a rectangle. But trust the developer: only one solution exists. 
Author:  nailhouse [ Tue Dec 15, 2015 11:25 pm ] 
Post subject:  Re: Killer Sudoku solving strategies 
Thank you for the explanation 
Author:  nailhouse [ Thu Dec 24, 2015 10:56 am ] 
Post subject:  Re: Killer Sudoku solving strategies 
It helped me today, solving the 'difficult' 8x8 calcudoku. 
Author:  marblevolcano [ Wed Jul 20, 2016 3:32 pm ] 
Post subject:  Re: Killer Sudoku solving strategies 
pnm wrote: b2b3 hold 2,5 (in some order)(not 3,4 because then the puzzle solution would no longer be unique) Same as nailhouse  I've used this a few times lately in the Holiday book. 
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