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- - **23% - 1063 seconds - 4x5 - I am wrong**
(*http://www.logic-puzzles.org/forum/showthread.php?t=251*)

23% - 1063 seconds - 4x5 - I am wrong2 Attachment(s)
Today I offer two puzzles... you may enjoy solving a very hard one, and perhaps you can tell me where I am going wrong?
1. Clue #1, 295K isn't closest, PLC isn't farthest, PLC isn't 295K. 2. Clues #2, 3, 5 and 9 are self-evident. 3. For now #4 only means Istryn isn't 51 light years. 4. #6, MKP isn't closest and 295K isn't farthest, MKP isn't 295K. Also observe MKP isn't 45. 5. #7, 345K isn't Theros and ZQ isn't 45. 6. #8 is self-evident, also Zhezios can't be 51 or 295K or 650K. 7. #10, ZQ isn't less than 47 and Cheelia not more than 47, Cheelia isn't ZQ. Observe ZQ can't be 49. 8. #11 is self-evident, and a bit redundant. 9. First pass through leaves only 1, 4, 6, 7 and 10 unresolved. Observe PLC isn't 45. From #1 we know it can't be 49 either. 10. All we have to work with is #7! "One orbits star ZQ" can only be Istryn or Theros, so "of… 345K" must point to Istryn. Eliminates 345K and 51. Istryn isn't HV or PLC so eliminate 345K from both HV and PLC. Only Istryn or Theros can be 45 so not Quael. 11. We're now done with #4, 243K must be 51. Since PLC isn't 51 it also isn't 243K, but 540K. Zhezios isn't 51 so can't be 243K but 540K, and since Zhezios is PLC and PLC conflicts with 49, remove 49 from Zhezios as well. 12. Observe Cheelia can't be 243K since it's not 51. MKP can't be 51 (not 243K) so per #6, 295K can't be 49. 13. #1 now indicates PLC can't be 47 so it must be 43 and cross that clue off, it helped us determine all the facts for Zhezios. Fill in the obvious X's and O's to complete the row and column. 14. We can see Cheelia is 47 light years. Carry the column into the row and ZQ is revealed at 51, also 243K. 15. Quael isn't ZQ so isn't 51, that would be Theros. Copy the facts from the row into the column. 16. #7 is complete, Theros is ZQ and 345K is 45. Observe Istryn is 45 so Quael is 49. Observe 47 is 295K so 49 is 650K. 17. #6 states MKP is 49 which is enough to finish the table, wrongly. VJD must be 47, but HV at 45 would seem to relate in the row to 345K but it can't be as we check the column. How did you do? And, do you see my error? Thanks! |

I'm with you until your step 10. I don't see how you deduced that the right side of clue 7 could only be Istryn or 345K.
At your step 10, I would replace the steps with the following. We're going to prove that PLC 120 can only be 43, but it is going to take a few steps to do that. One of the steps is going to involve looking at 51 and MKP 427 and noting that none of the planets can be associated with that particular combination. First use clue 7 to get a few more Xs. The left side doesn't help because the intersection of 345K and Theros doesn't have any other Xs in the row and column. The right side is loaded. The intersection of 45 and ZQ has 2 extra Xs in the row (MKP, PLC) and 2 Xs in the column (43, 49). Use this to deduce that Theros and 345K cannot be MKP or PLC. Other Xs can be placed as well, but for this exercise I am focused on the specific goal of showing that PLC can only be 43. Now we notice that Theros can only be VJD amd ZQ. More importantly, MKP can now only be Cheelia and Istryn. The other three columns for MKP are X'd out. 51 can only be Quael, Theros, and Zhezios. MKP cannot be any of these three since it can only be Cheelia and Istryn. So the combination of 51 and MKP doesn't work. That combination could not be associated with any of the planets. We can place an X in the intersection of 51 and MKP 491. Clue 6 says that MKP has to be 2 years more than 295K. So 295K can no longer be 49. Clue 1 says that 295K must be greater than PLC, and now 295K can only be 45 and 47. Since PLC can only be 43 and 47 at this point, the only way for PLC to be less than 295K is for PLC 120 to be 43. Things fall into place after this, and soon Theros will be 51. Clue 4 says that 243K must be Istryn or 51, and since 51 is Theros at this point, 243K has to be Istryn or Theros. This will lead to 243K = ZQ 75 = Theros. The solution is: 43 - Zhezios - PLC - 540K 45 - Quael - HV - 345K 47 - Cheelia- VJD - 295K 49 - Istryn - MKP - 650K 51 - Theros - ZQ - 243K |

First, your solution is correct and I don't want to talk about my fuzzy logic, ha.
I appreciated this a lot! A couple techniques are demonstrated: 1. We can simply and easily get a leg up on the "Of A and B, one is X and one is Y" clues by looking at the intersection of A/B and X/Y and the number of eliminations on their rows and columns. I never think that way but will start immediately :) 2. I've seen other puzzles where (somebody else found) the path forward relies on a pattern like you did here to eliminate 51 and MKP. It's a great one to watch for. 3. I'm intrigued by the notion of driving toward a key conclusion like, "We're going to prove that PLC 120 can only be 43". I do not know how often one could take that approach but it's clear when we're working hard for one X at a time, it'd be nice to know where we're going. Good stuff, thanks! |

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