Solving Logic Puzzles

[musicmeg222]

I've been solving logic puzzles online for awhile now. I understand most of the clues, but then get stuck and usually have to get a hint. It's hard to use all of the clues based on their wording. Any tips or suggestions for solving these on my own and not needing a hint?

[Kitku]

Usually when I'm stuck, it's because I failed to notice that somewhere there is a row or column that has got only one option left in another category (or, generalisation of this for larger numbers).

Beside that, look for clues that have something in common, for example, the same distance in the quantified variable:

1. Arnold paid 2$ more than Bradley.
2. Dalton paid 2$ more than the person who ordered water.

these two clues together give us information, that Bradley didn't order water, because if he did, Arnold and Dalton would have to be the same person.

Another example, if there are two clues in form of "of x and y, one is a and the other is b" that both mention one of the variables, sometimes you can squeeze out some additional restrains, e.g.

1. Of Arnold and the person who ordered root beer, one paid 24.99$ and the other ordered club sandwich
2. Of Arnold and the person who paid 26.99$, one ordered water and the other ordered cheeseburger.

From this, we can infer that club sandwich may be paired only with root beer or water in the beverages cathegory, and that the order that included cheeseburger must cost either 26.99$ or 24.99$
In this method you can also use clues in form of "x can be either a or b".
Generally, look for a variable that repeats itself in the same type of clues.

Hope this helps. If anything is unclear, let me know, I'll try to explain better.

[nitinbaisoya]

you should try hard first and if you still dont solve the puzzle then you should take help from chatgpt.

[pat44]

One of my favorite situations is when there are two items that are one unit away from each other. I guess this could be phrased as B = A+1. But you don't know what A is.
Once there are only two possibilities, for example, you know that A is either 1 or 2 gallons, and B is either 2 or 3 gallons, then you know that C, D, and E cannot be 2 gallons, because in either case, A or B has to take 2 gallons.

I think this is called a "pair"

[mpk620]

Another example, if there are two clues in form of "of x and y, one is a and the other is b" that both mention one of the variables, sometimes you can squeeze out some additional restrains, e.g.

1. Of Arnold and the person who ordered root beer, one paid 24.99$ and the other ordered club sandwich
2. Of Arnold and the person who paid 26.99$, one ordered water and the other ordered cheeseburger.

From this, we can infer that club sandwich may be paired only with root beer or water in the beverages cathegory, and that the order that included cheeseburger must cost either 26.99$ or 24.99$

I'm a little late to this, but how can you determine that the club sandwich is only paired with root beer or water and that the cheeseburger must be either $26.99 or $24.99? Or does making those inferences require that you include the first two clues of being $2 apart?

[JoshGrams]

Because the two clues have Arnold in common, you can walk through all the possibilities:

In clue 1, if Arnold ordered the club sandwich, then looking at clue 2 tells us that he ordered water (not the cheeseburger; two different sandwiches). If, on the other hand, he did NOT order the club sandwich, then clue 1 tells us that the person who ordered root beer was the one who ordered the club sandwich.

And similarly for the cheeseburger, starting with clue 2. If Arnold ordered the cheeseburger, clue 1 tells us he paid $24.99, and if he didn't then clue 2 tells us that the $26.99 person ordered the cheeseburger.

I generally don't bother looking for these because they're infrequent enough and I'm too slow at recognizing them, and usually the conflict eventually becomes visible in other ways, but I can see how they could be helpful if I was faster at seeing them...

[KatanaCS]

I'm a little late to this, but how can you determine that the club sandwich is only paired with root beer or water and that the cheeseburger must be either $26.99 or $24.99? Or does making those inferences require that you include the first two clues of being $2 apart?

I've always been hesitant about making a presumption on these, even though my instincts were screaming I could, but I never really took the time during a puzzle to work it out. I took a few minutes now to look at this and i can see that it is correct. If club sandwich is root beer, that's it. If it's Arnold, then of Arnold and $26.99, Arnold is not the cheeseburger, therefore club sandwich is water. So club sandwich is limited to root beer or water. Same for the cheeseburger - if it's 26.99 that's it, but if it's Arnold then since Arnold can't be club sandwich the cheeseburger is 24.99.

[Kitku]

I'm a little late to this, but how can you determine that the club sandwich is only paired with root beer or water and that the cheeseburger must be either $26.99 or $24.99? Or does making those inferences require that you include the first two clues of being $2 apart?

exactly as JoshGrams explained, and not, that inference doesn't require the difference you mentioned. I'll try to make it more clear and general by using colors for cateories, so we will have

A and B from one category, we will call the category GREEN, in my earlier example it could be the sandwiches
C and D from another category, ORANGE, in example: beverages
E and F - BLUE category, e.g. prices
and finally G from forth cateory, PURPLE, e.g. name of the customer
notice that in one of the four categories we have one item which occurs on two similary structured clues.

so, the clues can be rephrased as:

1. Of G and C, one is E and the other is A
2. Of G and F, one is D and the other is B.

notice the colours of the categories: PURPLE and GREEN stay on their sides of the clue, but BLUE and ORANGE swap places*

now, from 1st clue, A may either be paired with C or with G, but from the second clue G is paired with D or B, but A and B are in the same category, so they can't be paired, so if A is paired with G, then it is also paired with D => A is paired with C or D

and the second inference: from second clue, B is paired with F or G, but from the first clue G is paired with E or A,but A and B are in the same category, so they can't be paired, so if B is paired with G, then it is also paired with E => A is paired with E orF

So there it is in the most abstract version I could explain.

*Of course the clues won't allways be so nice to be so perfectly aligned to be easily spotted, so often it will be more like

1. Of C and G, one is E and the other is A
2. ...
3. ...
4. Of B and D, one is F and the other is G.

so I usually ignore them at first and only seek these relations out when I used everything more obvious