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clm
Posted on: Mon Apr 13, 2020 12:01 pm
Posts: 857 Joined: Fri May 13, 2011 6:51 pm
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Re: Exclusive puzzles
Thanks, michaele, for the puzzle and for your effort . The idea is very original and the puzzle very amused. However, I am sorry, but if I am right, the solution is not unique, I have found 2 solutions at least (not spending much time) and possibly there are more in my opinion. In addition to this, after applying analysis you find that the 11 small cages have a unique configuration as follows: "72x" = [3,3,8], "6+" = [2,4], "5x" = [1,5], "4x" = [1,1,4], "9x" = [1,3,3], "9+" = [2,2,5], "14+" = [4,5,5], "10+" = [1,2,3,4], "72x" = [2,6,6], "20x" = [1,4,5] and "4+" = [1,3], you conclude that the total sum of these cages (31 cells) is 100. Consequently, the big cage "177+" (with 33 cells) must have a sum of 288 - 100 = 188 and not 177 (since 288 = 8 x 36 is the total sum of the puzzle). Perhaps it would be interesting that Patrick tests this puzzle with the software to verify unicity, … .
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pnm
Posted on: Mon Apr 13, 2020 12:10 pm
Posts: 3305 Joined: Thu May 12, 2011 11:58 pm
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Re: Exclusive puzzles
clm wrote: Perhaps it would be interesting that Patrick tests this puzzle with the software to verify unicity, … . It's on my list, the software still has a problem with the very large cage (probably just some space allocation issue).
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michaele
Posted on: Mon Apr 13, 2020 1:08 pm
Posts: 149 Joined: Sun Jan 31, 2016 7:52 am
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Re: Exclusive puzzles
Quote: In addition to this, after applying analysis you find that the 11 small cages have a unique configuration as follows: "72x" = [3,3,8], "6+" = [2,4], "5x" = [1,5], "4x" = [1,1,4], "9x" = [1,3,3], "9+" = [2,2,5], "14+" = [4,5,5], "10+" = [1,2,3,4], "72x" = [2,6,6], "20x" = [1,4,5] and "4+" = [1,3], you conclude that the total sum of these cages (31 cells) is 100. Consequently, the big cage "177+" (with 33 cells) must have a sum of 288 - 100 = 188 and not 177 (since 288 = 8 x 36 is the total sum of the puzzle). You left out the 11+ cage, that would bring the total of the small cages to 111, leaving 177 for the large cage. I think there is only one solution, but I could be wrong, I created this puzzle very quickly, and will confess that I did not take as much time checking it as I usually would. If you can send me two solutions I would be interested to figure out what I did wrong. If I have made a mistake I will make some adjustments and try again.
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jaek
Posted on: Mon Apr 13, 2020 1:25 pm
Posts: 300 Joined: Fri Jun 17, 2011 8:15 pm
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Re: Exclusive puzzles
That was cool. I enjoyed it.
One thing about a cage that big is that I never used the fact that it was +177 to solve the puzzle; by the time that information would have become helpful I was well on toward completion and was just eliminating options using the basic "each number appears only once in each row/column" rule. That reminded me of a previous thread where someone smarter than me was wondering about how much information was necessary to solve a puzzle. In the current case, all the elements of that huge cage could be thought of as 'uncaged'.
Again, very cool.
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michaele
Posted on: Mon Apr 13, 2020 1:40 pm
Posts: 149 Joined: Sun Jan 31, 2016 7:52 am
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Re: Exclusive puzzles
Thank you jack.
It was an interesting exercise in creating a very large cage, but the puzzle is far too easy.
I will try creating another puzzle with a large cage, and I will try to make the large cage more significant to the solving method.
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bram
Posted on: Mon Apr 13, 2020 2:47 pm
Posts: 253 Joined: Tue May 24, 2011 4:55 pm
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Re: Exclusive puzzles
clm wrote: However, I am sorry, but if I am right, the solution is not unique, I have found 2 solutions at least (not spending much time) and possibly there are more in my opinion. michaele wrote: I think there is only one solution, but I could be wrong, I created this puzzle very quickly, and will confess that I did not take as much time checking it as I usually would. If you can send me two solutions I would be interested to figure out what I did wrong. If I have made a mistake I will make some adjustments and try again. For what it's worth, I think the puzzle has only one valid solution But I don't have time to revisit it right now
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clm
Posted on: Mon Apr 13, 2020 3:33 pm
Posts: 857 Joined: Fri May 13, 2011 6:51 pm
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Re: Exclusive puzzles
michaele wrote: Quote: In addition to this, after applying analysis you find that the 11 small cages have a unique configuration as follows: "72x" = [3,3,8], "6+" = [2,4], "5x" = [1,5], "4x" = [1,1,4], "9x" = [1,3,3], "9+" = [2,2,5], "14+" = [4,5,5], "10+" = [1,2,3,4], "72x" = [2,6,6], "20x" = [1,4,5] and "4+" = [1,3], you conclude that the total sum of these cages (31 cells) is 100. Consequently, the big cage "177+" (with 33 cells) must have a sum of 288 - 100 = 188 and not 177 (since 288 = 8 x 36 is the total sum of the puzzle). You left out the 11+ cage, that would bring the total of the small cages to 111, leaving 177 for the large cage. I think there is only one solution, but I could be wrong, I created this puzzle very quickly, and will confess that I did not take as much time checking it as I usually would. If you can send me two solutions I would be interested to figure out what I did wrong. If I have made a mistake I will make some adjustments and try again. You are right, and also bram with respect to the fact that the puzzle has only one solution. I apologize, I solved the puzzle without the cage 11 +, ... , I copied it to paper and simply did not draw that cage (I must be incubating some virus, ... ). The solution is unique of course and quickly obtained straight forward. And, as jaek comments, the information 177+ is irrelevant, so a no-op cage is also valid, that is, simply "177", as well as the cages "11+" and "10+" ("11" or "10" are also valid, since in these cases the operator must be an addition necessarily), and of course both "72" cages, etc.. Thanks.
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bram
Posted on: Mon Apr 13, 2020 3:43 pm
Posts: 253 Joined: Tue May 24, 2011 4:55 pm
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Re: Exclusive puzzles
jaek wrote: One thing about a cage that big is that I never used the fact that it was +177 to solve the puzzle; by the time that information would have become helpful I was well on toward completion and was just eliminating options using the basic "each number appears only once in each row/column" rule. Exactly michaele wrote: I will try creating another puzzle with a large cage, and I will try to make the large cage more significant to the solving method. Well, it's often frustrating when a large puzzle includes several large cages for which only the sums are given because those large sums tend to be unhelpful or only helpful in a tedious way Now what makes your puzzle stand out is precisely that it remains very entertaining in spite of taking that otherwise annoying feature to extremes As jaek has already stated, the trick is to think of the numbers in the humongous cage as "uncaged" and start solving that part of the puzzle in a sudoku-like manner when you have enough information to do so from solving the other cages
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michaele
Posted on: Tue Apr 14, 2020 2:19 am
Posts: 149 Joined: Sun Jan 31, 2016 7:52 am
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Re: Exclusive puzzles
Some people have mentioned that the large cage can be ignored and the puzzle can still be solved. I think that is a big problem with my puzzle, if the point of interest for the puzzle is the large cage then that cage should participate in the puzzle solving. So I have done a re-jig and I now think it is a better puzzle and the large cage plays a part in finding a solution. It should be more difficult to solve (if you ignore the previous version).
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bram
Posted on: Tue Apr 14, 2020 5:01 pm
Posts: 253 Joined: Tue May 24, 2011 4:55 pm
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Re: Exclusive puzzles
michaele wrote: So I have done a re-jig and I now think it is a better puzzle and the large cage plays a part in finding a solution. It should be more difficult to solve (if you ignore the previous version). I agree on both counts: The new version is (even) better than the original one and also more challenging. My recommendation to other puzzlers is to first solve the original version (which is still a great puzzle, and quite relaxing) and then the new one (without peeking at the original or its solution). Thanks a lot, michaele (Spoiler warning : Discussion of solution to new version follows.)In the new version it's quite simple and straightforward to fill in the 5+ cage, to determine which numbers belong in the 18 x cage (and fill in its 1s) and then (using the sum requirement of the colossal cage) to determine which numbers belong in the 288x cage (and fill in its lower cell and the 6+ and 4+ cages) Then comes a more challenging bit of analysis, which eluded me for some time and which I shouldn't really be revealing here so as to not completely spoil the puzzle I was frustrated at first and elated when I finally got it. A hint if you're stuck at this stage: By considering the (already determined) combination of numbers in the 18 x cage along with the possible combinations in th 7+ and 9+ cages, it's possible to determine which numbers belong in the 18 + cage and then to fill in the two leftmost columns along with the aforementioned cages After that the rest is just sudoku (like in the original version).
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