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

) 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

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.