Advanced Technique: Seeing Around Corners
Here's a technique for matching complementary exclusion sets in boxes that are on different rows and in different columns. I've detailed how this works in four images.
Complementary exclusion sets are when you have two sets of data that exclude, or complement, each other's values. Thus, there can be no link between the two. The pairing of these two values must therefore be false.
As you will see in this example:
Julia's exclusion set excludes everything except lime and indigo.
The $1500 exclusion set excludes lime and indigo ONLY.
Thus, Julia cannot have the $1500 hospital bill.
Complementary exclusion sets are typically easy to see. However, for this puzzle, the sub-grids for "Name/Color" and "$Money/Color" are on different rows. Further, one exclusion set is horizontal, and the other is vertical!
Matching up these sets involves a technique I call "Seeing Around Corners."
I have not encountered a puzzle, here, where this technique is the only one available to continue solving the puzzle, but it would be a real evil puzzle if it was.
Bear in mind, this is a really easy puzzle, and the exclusion sets are spelled out for you in successive clues. It's very easy to see this way. But what if it took several clues and techniques to reach this point? I had been wondering if this was a solving technique, but until I saw this easy puzzle, I didn't know if it would work.
Here's the puzzle. I filled it in up through clue 3 when I noticed the link between clues 2 and 3:
To prove that the two exclusion sets were complementary, I redrew the grid after swapping color and money. It's easy to see that the exclusion sets complement each other:
Now back to the original puzzle layout. Note how the two exclusion sets are on different rows and columns and that one is horizontal and the other vertical. Even so, you can link the two and eliminate one more value from the grid. All you have to learn, is how to see around the corners:
Instead of redrawing a grid to see complementary exclusion sets, just imagine rotating the upper-right box onto the second row. That's why I call it "seeing around corners". In the same way, the lower-left box can be rotated onto the second column. Note that the rotated boxes have two headings. Also note that the orientation of the headings matches the rotation. If you miss this, your conclusion will be incorrect:
I hope I explained this well enough for someone to learn from it.
Last edited by BillsBayou; 04-25-2013 at 02:42 PM.