View Full Version : Problem solving Puzzle with no positive clue

bugman

02-05-2012, 04:06 AM

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.

nonynezu

02-05-2012, 09:07 AM

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.

zenobia43

03-23-2012, 03:38 AM

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. :(

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 well-versed 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

zenobia43

04-09-2012, 11:35 PM

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.

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.

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

Either the astronomer who pointed their telescope at Mercury or the person who arrived on Friday dressed up as a zombie.

The astronomer who pointed their telescope at Saturn is not Mateo.

The astronomer who pointed their telescope at Jupiter arrived the day before the astronomer who pointed their telescope at Mercury.

The person who arrived on Friday didn't observe Saturn through their telescope.

The person who arrived on Friday is not Felix.

Among the person who arrived on Wednesday and the trick-or-treater who dressed up as a mad scientist, one is Mateo and the other is Skyler.

The five individuals are the trick-or-treater who dressed up as a werewolf, the astronomer who pointed their telescope at Mercury, Mateo, the person who arrived on Friday and the trick-or-treater who dressed up as a witch.

The trick-or-treater who dressed up as a werewolf didn't observe Saturn through their telescope.

The astronomer who pointed their telescope at Mars arrived the day before the astronomer who pointed their telescope at Jupiter.

The five individuals are the person who arrived on Thursday, Nathaniel, the astronomer who pointed their telescope at Jupiter, the trick-or-treater who dressed up as a mummy and the trick-or-treater who dressed up as a zombie.

Neither the astronomer who pointed their telescope at Mars nor the trick-or-treater who dressed up as a zombie is Karen.

zenobia43

04-11-2012, 04:51 PM

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?

yes, i normally solve the 5 persons clue first.

i managed to solve it under average time...

am just copy-pasting 1000 second+ and <25% puzzles here for reference

stanstar

06-13-2012, 09:54 PM

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

zenobia43

06-13-2012, 10:03 PM

Yes - but those two rows have to be in different category blocks.

I label the category blocks like this:

AB AC AD

DB DC

CB

So if you have two rows like you have shown with one of the rows in AB and the other in DB, then you know that a particular AD combination cannot be true.

For example, if the top row in your post was the intersection of Monday with First Names, and the bottom row was the intersection of bubble gum with First Names, then you know that Monday cannot be bubble gum.

For the tougher puzzles, you will have to use things like this to place an X that pops the whole thing loose.

This example focused on rows. The same principle applies to columns.

stanstar

06-15-2012, 07:59 PM

Hi Zenobia43 I just realised there was a page 2 so I didn't see your reply post.

I see what you mean now.

Stan

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