Logic Puzzle Forums Yet another advanced technique needed
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#1
04-10-2013, 02:55 PM
 BillsBayou Member Join Date: Mar 2013 Location: New Orleans Posts: 77
Yet another advanced technique needed

This puzzle has me STUMPED. The video and recent posts have gotten me only so far with this one.

I've come up with the following relationships in time:
375° +5m = 325°
MC +5m = 350°
375° +Xm = 4p
6p +5m = 400°
Where: p: people, MC: Mac and Cheese, m: minutes, X: Unknown amount

Of all of these, I only know that the Bean Casserole is 375°, but substituting those in give me no help.

What is the next logical step?

Logic-Meals.gif
#2
04-11-2013, 12:03 PM
 zenobia43 Senior Member Join Date: Mar 2012 Posts: 175

Another tough one and one that has a very tempting "what if" instead of pure logic.

There are two more Xs that can be added to your grid from clues 5 and 11.

Clue 5: mac and cheese cannot be 350 degrees.

Clue 11: 6 people cannot be 400 degrees.

Adding those two Xs doesn't seem to help much.

With that little empty rectangle in the AB category box (upper left), clue 12 unresolved, and clue 5 linking mac and cheese to the AC category box, I go for the "what if" method by choosing one of the clue 12 alternatives.

If 35 minutes = 4 people, then mac = 40 minutes, yams = 35 minutes = 325 degrees = 4. This forces baked ham = 350 degrees = 45 minutes.

Since 4 people now is 35 minutes, clue 11 dictates that 400 degrees can no longer be 40 minutes. With 350 degrees = 45 minutes, 400 degrees can only be 50 minutes.

Clue 11 then puts 6 people = 45 minutes. That's the same row as 350 degrees, and that's a problem.

In the grid, there is an X at 350 and 6. So that "what if" doesn't work.

We choose the other alternative for clue 12, and the solution is obtained.

I think the solution is:

30 minutes - bean - 375 - 8
35 minutes - mac - 325 - 2
40 minutes - yams - 350 - 4
45 minutes - ham - 425 - 6
50 minutes - potatoes - 400 - 5

There must be a pure logic solution for this, but the "what if" in this case was just too tempting.
#3
04-11-2013, 01:44 PM
 admin Administrator Join Date: Jul 2008 Posts: 182

The logic-only solution here is definitely a bit complex, but here's a quick stab at an explanation.

I'm starting off with the original screenshot, plus the two X's that Zenobia correctly pointed out could also be added (Clue 5: mac and cheese cannot be 350 degrees; Clue 11: 6 people cannot be 400 degrees.) It looks like the grid is then stuck at this point, but the way to break through is to compare clues 5 and 11 to each other:

mac and cheese --> 350 deg.
6 people --> 400 deg.

In my notations, --> means plus one increment (5 minutes) of baking time. (When a grid gets stuck and there are unfinished clues of the A >< B variety, I always write them all in the NOTES area so I can compare them and hopefully extract some useful data.)

Since 350 degress and 400 degrees cannot both have the same amount of baking time (as they're different options in the same category), and mac and cheese and 6 people are both 5 minutes less than the baking times of 350 deg. and 400 deg., that means mac and cheese and 6 people cannot have the same amount of baking time - and are therefore excludable from one another. This allows us to put an X into the yellow square.

That X then opens up 2 rows in the recipe/# of people subgrid where only the same two options are available (4 people and 6 people can only be baked ham and bean casserole, in some order). This allows us to X out any remaining open squares in those columns (baked ham and bean casserole) since we know they can only be 4 & 6. This allows us to put X's into the four blue squares.

Now (keeping in mind that the blue squares are X's), look at 350 degrees near the bottom of the grid. It can only be baked ham or candied yams. 2 people and 8 people cannot be either baken ham or candied yams - so they cannot be 350 degrees. This allows us to eliminate 350 degrees from 2 people and 8 people (X's in the pink squares), and that gives us a TRUE value for 4 people and 350 degrees. (forgot to color it in on the grid, sorry)

ALMOST THERE!

Now, since 4 people == 350 degrees, and 350 degrees cannot be 35 minutes, we can X out the light green square near the top right of the grid to indicate that 35 minutes CANNOT be 4 people. And that brings us back to clue #12 - if 35 minutes =/= 4 people, then 35 minutes must be mac and cheese. And from there the grid cascades to a complete solve.

log.jpg
#4
04-11-2013, 02:29 PM
 BillsBayou Member Join Date: Mar 2013 Location: New Orleans Posts: 77

zenobia43, thanks for pointing out those missing squares. I keep having to go back and fix those clue types in my solves.

Admin, thanks for the tips on figuring out the relationships. In the list of requirements I had:
Quote:
 Originally Posted by BillsBayou 375° +5m = 325° MC +5m = 350° 375° +Xm = 4p 6p +5m = 400° Attachment 25
I had missed that point. This is another tool in the tool chest.

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