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Difficult 6x6 Thursday July 21st https://www.calcudoku.org/forum/viewtopic.php?f=16&t=811 
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Author:  paulv66 [ Thu Jul 21, 2016 3:52 pm ] 
Post subject:  Difficult 6x6 Thursday July 21st 
I found it very difficult to get to grips with today's 6x6. It was one of those patterned ones, with a 4x4 central core and 4 L shaped cages around the outside. I finally worked it out, but it took me longer than it took me to do today's 12x12. Did anyone else struggle with this one, or was it just me? 
Author:  jpoos [ Thu Jul 21, 2016 4:16 pm ] 
Post subject:  Re: Difficult 6x6 Thursday July 21st 
paulv66 wrote: I found it very difficult to get to grips with today's 6x6. It was one of those patterned ones, with a 4x4 central core and 4 L shaped cages around the outside. I finally worked it out, but it took me longer than it took me to do today's 12x12. Did anyone else struggle with this one, or was it just me? I took it down fairly quickly with some educated guessing. I think I encountered three dead ends, which gave me enough information to solve it in less than five minutes. Edit: looking in my solved puzzles history, I'm seeing that it took me about 2 minutes and 30 seconds, but it took me longer the second time just now. 
Author:  jaek [ Thu Jul 21, 2016 7:24 pm ] 
Post subject:  Re: Difficult 6x6 Thursday July 21st 
paulv66 wrote: I found it very difficult to get to grips with today's 6x6. It was one of those patterned ones, with a 4x4 central core and 4 L shaped cages around the outside. I finally worked it out, but it took me longer than it took me to do today's 12x12. Did anyone else struggle with this one, or was it just me? I remember getting the easy parts in place  more or less filling in the central square  and then hitting a road block. But it didn't take so long that I remember being discouraged. I think I ended up using the rightmost 17+ in relation to the 22+. There are definitely times when the answers just don't come though. Good luck. 
Author:  clm [ Thu Jul 21, 2016 8:07 pm ] 
Post subject:  Re: Difficult 6x6 Thursday July 21st 
paulv66 wrote: I found it very difficult to get to grips with today's 6x6. It was one of those patterned ones, with a 4x4 central core and 4 L shaped cages around the outside. I finally worked it out, but it took me longer than it took me to do today's 12x12. Did anyone else struggle with this one, or was it just me? Hi, paulv66. Since b5c5 = [1,3] >>> e4 = 1, e5 = 2. Of course b4c4 = [5,6]. The cage "3" in d4d5 can be [2,5] or [3,6]. You can quickly eliminate [3,6], because then a3 + a4 = 9 (that is, 17 + 4 + 6 + 2 + 22  42, being 42 the sum of the two lower rows). Consequently, in this hypothesis, a3 = 5, a4 = 4 and no number would now be possible in a5. Then d4 = 2, d5 = 5. As a consequence d3 = 1, e3 = 4 and d2e2 = [3,6] (unique). And this means that cage "4" must be [2,6] (with c2 = 2, c3 = 6) (because the 4x4 central core has a total sum of 126  3 x 17  22 = 53, that is, the fulll grid minus the four Lshape cages, producing a sum of 8 for this cage). At the same time, and similarly as before, now a3 + a4 = 17 + 4 + 5 + 2 + 22  42 = 8 >>> a3 = 5, a4 = 3, then f4 = 4 >>> a5 = 4 >>> f5 = 6. And also b4 = 6, c4 = 5. Clearly, the 3 of row 3 is not possible in b3 so b3 = 2, b2 = 4 (f2 = 3). And f2 = 5, a2 = 1. Since a6 + b6 = 5 >>> a6 = 2, b6 = 3 (obviously a 6 in a6 would have been excessive for the "17+" cage ) and the rest is quickly filled (f1 = 2, f6 = 1, ... ). Finally, you may observe something that you could find useful in the future: The sum of the corners in this case is 11 (6 + 2 + 2 + 1). As we know (the demonstration is in other places in the Forum), the 4x4 central core has always a sum which is equal to the sum of the corners + 2 complete lines, that is: 53 = 11 + 42 (in a 6x6 puzzle). 
Author:  paulv66 [ Thu Jul 21, 2016 8:54 pm ] 
Post subject:  Re: Difficult 6x6 Thursday July 21st 
Thanks folks, particularly clm for your detailed analysis. I think the reason I had so much trouble was because I went through the centre core quite quickly without thinking it through fully. I had figured out that the four corner cells must add up to 11, although not quite as simply as clm's formula. (My approach was 4 x 21  3 x 17  22). I think I'll be ok with this type of puzzle going forward, but in my case today it was definitely a case of more haste, less speed. 
Author:  marblevolcano [ Mon Jul 25, 2016 10:02 pm ] 
Post subject:  Re: Difficult 6x6 Thursday July 21st 
jpoos wrote: I took it down fairly quickly with some educated guessing. I think I encountered three dead ends, which gave me enough information to solve it in less than five minutes. Yeah, I guessed a few times, but it eventually led me to an answer in... oh, I don't know, 20 minutes? I actually forget how long it took. In fact, I may have given up on it the first time, only to solve it later 
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