Calcudoku puzzle forumhttps://www.calcudoku.org/forum/ Killer Sudoku solving strategieshttps://www.calcudoku.org/forum/viewtopic.php?f=19&t=756 Page 1 of 1

 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 otherpuzzlers 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 = 3After 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...What do you mean with this?

 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...What do you mean with this?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.

 Page 1 of 1 All times are UTC + 1 hour [ DST ] Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Grouphttp://www.phpbb.com/