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 patterned 8x8, addition only 
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Posted on: Wed Sep 09, 2015 8:35 pm




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Joined: Thu May 12, 2011 11:58 pm
 patterned 8x8, addition only
will probably be adding a set of puzzles like the one below to the bonus puzzle pool... [cool]

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Posted on: Wed Sep 09, 2015 10:34 pm




Posts: 193
Joined: Tue May 24, 2011 4:55 pm
Post Re: patterned 8x8, addition only
Cool! [thumbup]

This puzzle took more time than an ordinary bonus puzzle. At one point I had to resort to trial and error [sad] but happily one of the alternatives quickly led to a contradiction and could be ruled out [smile]


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Posted on: Thu Sep 10, 2015 2:06 am




Posts: 498
Location: Ladysmith, BC, Canada
Joined: Fri May 13, 2011 1:37 am
Post Re: patterned 8x8, addition only
Well, if bram had trouble with it then I can look forward to not being able to solve it......I guess this is as good a time to start cutting back on my time spent on this site.....thank you for helping me make this decision.


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Posted on: Thu Sep 10, 2015 8:43 am




Posts: 2215
Joined: Thu May 12, 2011 11:58 pm
Post Re: patterned 8x8, addition only
beaker wrote:
I guess this is as good a time to start cutting back on my time spent on this site.....thank you for helping me make this decision.

This is a running theme in beaker's replies :)

I didn't do the puzzle myself, but I'm thinking that with this type of
puzzle there are always possibilities for cells that are "sticking out",
and using the fact that 1 + 2 + ... + 8 = 36 ?


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Posted on: Thu Sep 10, 2015 1:00 pm




Posts: 193
Joined: Tue May 24, 2011 4:55 pm
Post Re: patterned 8x8, addition only
pnm wrote:
I didn't do the puzzle myself, but I'm thinking that with this type of
puzzle there are always possibilities for cells that are "sticking out",
and using the fact that 1 + 2 + ... + 8 = 36 ?
Yes, those are the basic tools when dealing with this kind of puzzle. And I don't mean to say that addition-only patterned 8x8s shouldn't be added to the pool of bonus puzzles or to discourage anyone from trying out this kind of challenge. Indeed, when the puzzles can be solved online it will be much easier (for us not-quite-clm-analytical-level puzzlers [smile]) to do a bit of trial and error than it would if we were using pen and paper: We can just click on "Save for later", try out our guesses and reload the puzzle if they don't work out [wink]


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Posted on: Thu Sep 10, 2015 10:45 pm




Posts: 694
Joined: Fri May 13, 2011 6:51 pm
Post Re: patterned 8x8, addition only
bram wrote:
pnm wrote:
I didn't do the puzzle myself, but I'm thinking that with this type of
puzzle there are always possibilities for cells that are "sticking out",
and using the fact that 1 + 2 + ... + 8 = 36 ?
Yes, those are the basic tools when dealing with this kind of puzzle. And I don't mean to say that addition-only patterned 8x8s shouldn't be added to the pool of bonus puzzles or to discourage anyone from trying out this kind of challenge. Indeed, when the puzzles can be solved online it will be much easier (for us not-quite-clm-analytical-level puzzlers [smile]) to do a bit of trial and error than it would if we were using pen and paper: We can just click on "Save for later", try out our guesses and reload the puzzle if they don't work out [wink]


Very interesting puzzle, anyway. Particurlarly myself I have not a preference, I think it could appear as bonus (the difficulty is compensated with more time to solve it, usually we have two or three days for the bonus puzzle) or as a regular puzzle. In general, the single operator puzzles (mainly addition only) could be very difficult, in 8x8's, 9x9's, ... , specially with large cages (12-cell and two 6-cell in this case).

This one is not specially difficult and it is very curious since you quickly "prepare" the double border arriving to the real difficulty which is the inner ring "52+". There are several points in this 2-rings border with only "two branches" so TAE would drive to a "power of two" number of ways to reach the solution.

The "addition rule", 1 + 2 + ... + 8 = 36, is here necessary for the first part of the process but later, if we plan an analytical solution, we need different tools and this puzzle, due to its caracteristics (some "simmetry"), is suitable in my opinion and invites us to use the "segmentation" idea ("Solving strategies and tips"), that is, the 16 numbers in the inner 4x4 box must be exactly the same 16 numbers that appear in the four 2x2 boxes in the corners (of course the sum and the product of both sets must be identical). However, to add emotion, the lower right corner is not absolutely defined in its content (it is clear, once the border has been "solved", that g7 = 4 and h7 = 3, but g8-h8 could be [4,5] or [3,6]) creating two possible pools for the 16 numbers in the inner area and consequently two possible vias to the solution.


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Posted on: Mon Sep 14, 2015 6:36 pm




Posts: 498
Location: Ladysmith, BC, Canada
Joined: Fri May 13, 2011 1:37 am
Post Re: patterned 8x8, addition only
Interesting that both clm and bram think these new 8x8's are difficult......I used your suggestion and their's and tried this puzzle 3 times but failed to find the solution........I had always thought that the Bonus Puzzle was a reward of sorts for having attained a certain number of points and hence would be solvable by any user.......if these new puzzles can't be solved by all users then some might not want to subscribe to this site which would be [sad] as this site has evolved into a fun and somewhat challenging place to spend some time each day!
I would like to have seen some more larger twins or some no op twins instead of these new multicelled (which have always given me "fits") 8's or even possibly "bitwise OR" twins if that is possible.


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