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Trial and error https://www.calcudoku.org/forum/viewtopic.php?f=2&t=65 
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Author:  ineedaname [ Wed Oct 12, 2011 2:01 am ] 
Post subject:  Re: Trial and error 
One day I'll find time to read these properly & try to get my head around what is being said as it is fascinating to read. I usually manage to do from 4 easy up to 6 medium but must admit I do find teh 5 difficult usually the most troublesome of teh lot on some days. the 6 difficult onwards I print out & need to pencil mark it to work out. The 7 & 8 puzzles are the same & depending on how much time I have at night to do them usually determines if I solve it or not but a lot of the time I give up on it . Modulo & bitwise I have absolutely no idea on so don't even look at them. I'm sure if I sit down & have a good read over all of the tips & help given so far would enhance my puzzle solving ability but I just do them to keep the old brain ticking over which is why I have a crack at teh timed puzzles if I get time even though I'm no chance in finishing in the points but I would still do what I do know with points or not as I just enjoy the challenge. 
Author:  sneaklyfox [ Wed Oct 12, 2011 3:19 am ] 
Post subject:  Re: Trial and error 
bitwise isn't too bad but I find modulo among the hardest because of the many possibilities involved. Plus, considering that I am a somewhat careless person when it comes to mathematics (as you can see somewhere in another post), there's a good chance I'll accidentally miss a possibility and have to start all over again. 
Author:  picklepep [ Wed Oct 12, 2011 4:02 am ] 
Post subject:  Re: Trial and error 
rossiniman wrote: Whoa! The 7 subtractions are wonderful! Don't disfigure them! Technique I find useful is to figure out where the 3 evens and 4 odds in each row/column can go, then rule out possibilities by seeing whether any of the options put too many or too few odds or evens in the next row/column, as a result of even cages having two of the same and odd cages having one of each. I used this technique for the first time today! Thanx for the tip, cut my solving time by about ten minutes! 
Author:  starling [ Wed Oct 12, 2011 5:27 am ] 
Post subject:  Re: Trial and error 
sneaklyfox wrote: bitwise isn't too bad but I find modulo among the hardest because of the many possibilities involved. Plus, considering that I am a somewhat careless person when it comes to mathematics (as you can see somewhere in another post), there's a good chance I'll accidentally miss a possibility and have to start all over again. I'll agree with both of these. I find bitwise the easiest of the three extra operators, since you can almost instantly place all the 8's, and a large number of the 7's. Meanwhile with modulo there are seemingly fewer things with useful information in multiple places. 
Author:  jomapil [ Wed Oct 12, 2011 10:30 am ] 
Post subject:  Re: Trial and error 
I also agree that modulo is the hardest and bitwise the easiest. To gain more adherents of these special puzzles it would be valuable anyone explain, with more details and examples, these puzzles. As a curiosity, the total number of different possibilities (for 8x8) are Bitwise 2cells 28 Bitwise 3cells 112 Mod 2cells 56 As there are many puzzlers that haven't mathematical formation it would be helpful to make available the respective tables. I hope, hopefully, that Patrick don't remember to do module 3cells 
Author:  pnm [ Wed Oct 12, 2011 11:17 am ] 
Post subject:  Re: Trial and error 
jomapil wrote: I also agree that modulo is the hardest and bitwise the easiest. The real reason for this is that I set the difficulty level for the bitwise OR puzzle to be substantially lower, just to make it easier for people to get used to the new operator. It was meant to be temporary, I just forgot about it. So I guess I should adjust that upwards now Patrick 
Author:  starling [ Wed Oct 12, 2011 1:03 pm ] 
Post subject:  Re: Trial and error 
jomapil wrote: I also agree that modulo is the hardest and bitwise the easiest. To gain more adherents of these special puzzles it would be valuable anyone explain, with more details and examples, these puzzles. As a curiosity, the total number of different possibilities (for 8x8) are Bitwise 2cells 28 Bitwise 3cells 112 Mod 2cells 56 As there are many puzzlers that haven't mathematical formation it would be helpful to make available the respective tables. I hope, hopefully, that Patrick don't remember to do module 3cells Okay, I'm curious, why is this any different than just 8*7 (Assuming a fixed cell shape) in the case of 2 cell bitwise cages by the fundamental counting theorem? They have the same number of possibilities, it's just that a bitwise cage gives you more information to resolving it. As for any 3 (Except division and subtraction), assuming it's L shaped, it's 8*1*7+8*7*6, which is the number in which the two branches are equal, and the nexus different, plus the number with all three different. This is 392 for an L shaped, and for 3 in a row, it's 6*7*8, which is 336. All of this, mind you, is still the fundamental counting theorem for the sake of proof. But the thing is that the rate at which this can be reduced is drastically different in a bitwise cage. 1 doesn't exist. 2 doesn't either. 3 contains only 1's and 3's, so there are 2 combinations in a 2 cell cage, and 2 in a 3 cell cage. 4 doesn't exist. 5 contains only 1's, 4's, and 5's, making 6 combinations for a 2 cell cage, and 12 combinations for a 3 cell cage. 6 contains only 2's, 4's, and 6's, making 6 combinations for a 2 cell cage, and 12 combinations for a 3 cell cage. 7 can contain absolutely anything < 8. But it's still dramatically reduced because it must contain at least 1 number > 3. There are 24 possible 2 cell solutions, and a lot more 3 cell than I care to calculate, enough to the point at which you won't get much of anywhere by trying to eliminate possibilities on an l shaped 3 cell 7 bitwise or. 8 doesn't exist. 915 in an 8x8 is just 8 and the difference in 8 and the cage number. So 13 is 8 and 5 in two cells, and in 3 is 8 + any of the options for 5 for two cells from earlier, etc. Basically, even with the difficulty set lower as it apparently was, bitwise or is still fundamentally easier than any of the other functions at the size we're doing it (Personally, I'll take easier bitwise puzzles in exchange for not having to do a 16x16 Modulo puzzle. At that point, it wouldn't matter which function was harder, since I don't think I'd have the patience to solve any of them.). 
Author:  sneaklyfox [ Wed Oct 12, 2011 6:38 pm ] 
Post subject:  Re: Trial and error 
starling wrote: 3 contains only 1's and 3's, so there are 2 combinations in a 2 cell cage, and 2 in a 3 cell cage. Actually 3 contains 1's, 2's and 3's. 
Author:  sneaklyfox [ Wed Oct 12, 2011 6:51 pm ] 
Post subject:  Re: Trial and error 
Continuing starling's comparison of bitwise and modulo... With 2 cell cages but not counting the permutations (just multiply by 2 if you want to include that), in an 8x8... mod0 has 12 combinations mod1 has 16 combinations mod2 has 11 combinations mod3 has 7 combinations mod4 has 4 combinations mod5 has 3 combinations mod6 has 2 combinations mod7 has 1 combination mod8 doesn't exist 
Author:  honkhonk [ Wed Oct 12, 2011 9:51 pm ] 
Post subject:  Re: Trial and error 
Earlier discussion on the bitwise OR http://www.calcudoku.org/forum/viewtopic.php?f=3&t=63 
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