#1




Problem solving Puzzle with no positive clue
I encountered a puzzle with all "nots" and no "is's" This left a grid with red x's but not enough on any rank or file to put in a green. What is the strategy to solve such a case without guessing? I redid the grid 10 times thinking I made a mistake and ended up having to make a guess.

#2




If you still have the clues, someone could probably give you a suggestion more specific to the puzzle you had trouble with, but one thought is that sometimes clues can be combined. For example, in a 4x4 puzzle suppose we know that "Alice drinks neither tea nor coffee", "Alice doesn't play either the violin or piano", and "the flutist doesn't like soda or juice". So far we have eliminated only two of the four options in any column or row. However, notice that since Alice doesn't drink tea or coffee, she must drink either soda or juice, which means she cannot be the flutist. That leaves only one option for the instrument that Alice plays.

#3




When I encounter a puzzle that results in all X's and no positive clues, I usually do the following steps:
1. Check for intersections as described in this thread's first reply. I look for category blocks that have a lot of X's  especially ones that have a lot of rows or columns with only two remaining openings. If you find two rows or columns that, when combined, have an X in every cell, you know that combination can never be true. 2. Check for columns in the category blocks in the top row that are related by an order clue stating that one element is a fixed distance from the other. A typical example would be something like: "Jason arrived one day later than Megan." If only two days remain open in each column, then you can X out the overlapping day in the other columns Example: If Jason can only be Tuesday and Wednesday, and Megan can only be Monday and Tuesday, then either Jason or Megan has to be Tuesday. Therefore, no other person can be Tuesday. 3. Check for situations where two members of a category have only two choices left, and those choices are the same for both members. Example: Both Kaitlin and Nehemiah can only be Monday and Tuesday. All the other days for both of these names are X'd out. This means that either Kaitlin is Monday and Nehemiah is Tuesday, or Kaitlin is Tuesday and Nehemiah is Monday. Either way, no other name can be associated with Monday or Tuesday. Usually when I find one of these, I can place a lot of Xs. 4. Go back and get some more information from the ordering clues and the "Of Noah and the person who arrived on Monday, one likes shopping, and the other lives east of city hall." Using this "Of Noah ..." clue as a concrete example: a. Determine which days of the week are possible for Noah. We already know that Noah cannot be Monday from the clue. If only Tuesday and Wednesday are the only remaining possibilities for Noah, then for the proposition to be true, shopping and east of city hall can only be Monday, Tuesday, or Wednesday. In practice, I look for X's in Noah's row or column that are in addition to Monday, and then I add the corresponding X's to shopping and east. b., c., d. Do that for each of the four parts of the "Of Noah ..." clue. You will usually get several X's. I.e. (b.) determine which first names are possible for Monday, (c.) determine which locations are possible for shopping, and (d.) determine which hobbies are possible for east of city hall. There is probably a pattern match technique for doing this logic, but I haven't progressed this far yet. Still a beginner. e. Do the same sort of thing for the ordering clues. You might find a relationship such as: B1 or B2 arrived later than B2 or B3. Where B is a particular category. Normally the above situation would have 4 possible combinations. B1 later than B2, B1 later than B3, etc. However, since B2 cannot be later than itself, this can result in another X. 5. Remember to place an X for the "Either the person who arrived on Tuesday or the clarinet player ..." or "Neither the person who arrived on Tuesday nor the clarinet player ..." clues. The two category members mentioned are not the same person. This is obvious when the two members are in the same category, but it's not so obvious when they are in different categories. 6. If all of the above still doesn't lead to the solution, then look in each category block for situations where a category member only has a couple choices left. Look in the grid to see what would happen if each choice was taken. Sometimes, the constraints in the other category blocks will exclude all the choices in a particular category. This is a variation of #1 above where a combination results in Xs in every cell. Example: Categories are Weekday, First Name, Holiday, and Gum. If you get to the point where the remaining choices for Adam are Juicy Fruit or Dentine, and picking Juicy Fruit would exclude Adam from any of the holidays (because of existing constraints in the grid), then Adam cannot be Juicy Fruit. Adam has to be associated with one element in each of the categories, and in this example, Adam has to be associated with a holiday. 7. Finally, if after doing all of the above the puzzle still cannot be solved without a guess of some sort, in my case, it is usually because I've missed an X or I've placed an X in the wrong place. I usually have to push the reset button and try again. Last edited by zenobia43; 03292012 at 05:10 AM. 
#4




25% solved, 1000 second average, no direct solution
This is the 2nd one I have got over the last few days. I forgot to save the first one (it had no positive clues)... this is the 2nd:
See if this can be solved without taking a chance: This Puzzle's Statistics Success Rate: 25.9% Average Time: 1008.6 seconds Record Time: 148 seconds (pootle) Either Rose or Pierce arrived on Wednesday. The person who arrived on Thursday isn't wellversed in Perl. Neither Pierce nor the person who started the exploding whale craze specializes in PHP applications. The person who arrived on Thursday is Rose. The person who arrived on Friday is not Marley. The Cold Fusion programmer arrived the day before the person who started the exploding whale craze. Among the person who started the lolcat craze and the Flash programmer, one is Marley and the other arrived on Monday. The person who arrived on Wednesday didn't start the will it blend craze. The person who started the dancing baby craze is not Pierce. The five individuals are Pierce, the person who started the lolcat craze, Roberto, the PHP programmer and the person who arrived on Thursday. The PHP programmer didn't start the will it blend craze. Monday Tuesday Wednesday Thursday Friday First Names Marley Nayeli Pierce Roberto Rose Internet Crazes dancing baby exploding whale lolcat rickrolling will it blend Languages Cold Fusion Flash PHP Perl Python Here's what I have so far: Monday  (Nayeli/Roberto)  {not exploding whale and rickrolling}  {not cold fusion} Tuesday  Marley  (dancing baby/lolcat)  {not cold fusion} Wednesday  Pierce  Rickrolling  {not flash and php} Thursday  Rose  (exploding whale/will it blend)  (cold fusion/python) Friday  (Nayeli/Roberto)  {not lolcat and rickrolling}  {not cold fusion and flash} EDIT: Apparently, there is a hidden clue which indicates exclusivity between PHP, Flash and lolcat among Mon/Tue. This opens up a line to indicate PHP = Friday and the puzzle is solved: mon  roberto  will it blend  flash tue  marley  lolcat  perl wed  pierce  rickroll  cold fusion thu  rose  expl whale  python fri  nayeli  dancing  php Last edited by ndd; 04092012 at 06:27 PM. 
#5




From the state you indicated, you can squeeze more information from Clue # 7
# 7: "Among the person who started the lolcat craze and the Flash programmer, one is Marley and the other arrived on Monday." Marley is already associated with Tuesday. So lolcat and Flash have to be either Monday or Tuesday. From clue # 10, lolcat can never be PHP (all five individuals are different people). So after using this fact in the left side of # 7, Marley and Monday have to be associated with either Flash or something other than PHP. I.e. Marley and Monday cannot be PHP. If I got this right, then placing all these additional constraints will lead to the solution. 
#6




Yes, I finally managed to solve it with that info (as shown in the edit part of my post at the end)
The first puzzle I had got was even more difficult. There was not a single positive clue. I did many trial and errors and by the time I got it, I had forgotten to save it. 
#7




Found another one
Success Rate: 25.3%
Average Time: 1323.2 seconds Record Time: 272 seconds (Mari) Monday Tuesday Wednesday Thursday Friday First Names Felix Karen Mateo Nathaniel Skyler Planets Jupiter Mars Mercury Saturn Venus Costumes mad scientist mummy werewolf witch zombie

#8




From clue #1, Mercury and Friday cannot be the same person. Have you included that constraint?
From clue #11, Mars and zombie cannot be the same person. Have you included that constraint? Clues #7 and #10 provide lots of constraints. I would normally put these in first and then incorporate the other clues. What state is your solution grid in when you have to make a guess? 
#9




yes, i normally solve the 5 persons clue first.
i managed to solve it under average time... am just copypasting 1000 second+ and <25% puzzles here for reference 
#10




Hi Zenobia43 You said in paragraph 1. I look for category blocks that have a lot of X's  especially ones that have a lot of rows or columns with only two remaining openings. If you find two rows or columns that, when combined, have an X in every cell, you know that combination can never be true.
you don't mean like this do you? : X _ X X _ X X _ _ X Stan 
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