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riverfloat45 12-30-2013 03:57 PM

Cannot solve common logic conundrum
 
Hello from a new, self-taught solver. I have progressed to moderate level and am stuck wrapping my mind around a common puzzle situation. The hint is not detailed enough for this stuck mind! I do not use hints normally, but I keep running into this wall and thought the hint would help as a guide.

The puzzle reference number: Puzzle #540475

The logic:
Of the diner who paid $4.99 and Lee, one ordered the hamburger and the other had the iced tea.

The hint:
If Lee does not equal $6.99, and hamburger and iced tea can only be paired with either $4.99 or Lee, then hamburger cannot be equal to $6.99. Mark the highlighted cell as FALSE. I am noting that both iced tea and hamburger were available for Lee at this time, as well as both available for $4.99 and $6.99.

Can someone please explain, in layman's terms, why this must be so? In my apparently stubborn mind, why cannot Lee have been the iced tea, therefore still allowing the hamburger for $6.99? I am aware this is an awkward explanation of my problem.
Any help is most appreciated.

zenobia43 12-30-2013 04:33 PM

There are lots of posts explaining this type of clue.

Think of this clue as having a left side ($4.99 and Lee) and a right side (hamburger and iced tea).

In this case, if $4.99 is hamburger, then Lee must be iced tea.

If $4.99 is iced tea, then Lee must be hamburger.

That's the logic being expressed by the clue.

So if we find that Lee cannot be $6.99, since we know that $4.99 cannot be $6.99, then the whole left side cannot be $6.99.

Said another way: The only way for the left side to have a $6.99 option is for Lee to be $6.99.

Now since the right side can only be one of the two options on the left, if the left side can never be $6.99, then neither of the two options on the right can be $6.99.

The hint spells this out. It is stating that Lee cannot be $6.99, so one of the other clues must have provided this piece of the logic. The hint goes on to conclude that since the left side can never be $6.99, then hamburger cannot be $6.99. It turns out that iced tea can never be $6.99 either. So you can actually place two Xs for this hint.

To answer your other question:

"why cannot Lee have been the iced tea, therefore still allowing the hamburger for $6.99?"

If Lee is the iced tea, then the two remaining options from the left and right side must be paired. Thus, $4.99 must be hamburger.

This "double exclusive or" clue is usually a source of a lot of Xs, and if you encounter the clue at the right time, you will have a constraint in the solution grid that allows you to get two positives.

The "single exclusive or" clue (Lee is either iced tea or hamburger) is very similar, and you can usually get more Xs by looking at the intersection of the two options in the clue's right side. If the two options are in different categories, Xs in the row and column where the two options intersect can be transfered to the single option of the clue's left side.

The layman logic description for the single exclusive or clue is about the same: If the right side can never be [whatever], then the left side cannot be that option either.

riverfloat45 12-30-2013 04:59 PM

OP thanks you!
 
I see now that I was overthinking the problem. Your detailed explanation did the trick. You, sir or madam, have my gratitude!


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