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Paladin · Joined: 10 Feb 2006 Posts: 15

This puzzle appeared in the May 3, 2008 issue of the St. Louis Post-Dispatch. The initial grid configuration was:

008009000500600030701000050400072000003000900000890006010000607070004001000900500

Using elementary solving techniques, the grid was reduced to this configuration:

Victor · Joined: 29 Sep 2005 Posts: 207 Location: NI

Hmm - Sorry, I don't think your colouring is valid. True colouring chains require a conjugate (strong) link each time, but your second move from r8c7 to r8c1 isn't, for there are three 8s in the row. (Or, if you wanted to do a kite-type strong-weak-strong move, you've a link too many.) Also, a colouring chain needs an odd number of links, but yours has 4.

keith · Posted: Wed May 07, 2008 11:40 pm Post subject:

Paladin,

These Saturday puzzles are usually discussed on this site as "DB Puzzles". Your one is at

http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=2514

Keith

Paladin · Joined: 10 Feb 2006 Posts: 15

Thank you, Victor, for your help with "colouring" and your XY wing solution. Hopefully I can get this colouring technique down as I study your explanation.

Thank you, Keith, for your reference.

Paladin

Victor · Joined: 29 Sep 2005 Posts: 207 Location: NI

Paladin, thanks for the thanks! Maybe worth reading Nataraj's comments in http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=2527&sid=f0d5432b811e95d057aa15ae00c0fa21

I'll repeat more or less waht he said anyway. Suppose you've two cells A = (2,3) & B = (2,8), with no instant connection. They both 'see' another cell with a 2 in it & so you'd like to find a chain connecting A & B, so that you could eliminate that other 2. The wrong way is to start by saying A = 2 and therefore ... , because even if that got you to B not equal to 2, well, so what? The right way to start is to say A <> 2, and try to find a chain that proves that now B = 2. All ordinary chains work in both directions, and so you'd then be guaranteed that one or other 2 is correct.

That's how I look at colouring chains - I just run along them looking at the digit of interest: false / true / false /true. . . until maybe I get to a point where the last one is a 'true' AND the start and endpoint both see another of the digits to be eliminated. (Some people use actual colours I think - hence the name.) These colouring chains use only conjugate (strong) links - every time there's only two of the digit in the relevant row/column/house. But most fancier chains use alternate strong and weak links - and are often given fancy names such as 'kite'.