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Old 01-09-2005, 03:57 PM   #1 (permalink)
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Default Help, Please!

I know this is a Tech-Forum and I'll take heat for this, but I really need help with my schoolwork. There is this one problem I can't figure out and it is for math. Can you guys help?

This is how the problem goes.

Three red hats and three blue hats are packed in three boxes, with two hats to a box. The boxes are all labeled incorrectly. To determine what each box actually contains, you may select one bohat from one box, without looking at the contents of that box. Explain how this will allow you to determine the contents of each box. (Hint: List all possible solutions; then use logic to solve.)

Box 1 has label Red & Red, Box 1 is Blue & Blue, Box 3 is Red & Blue; remember they are labeled incorrectly.

What I can't understand is what solutions, let alone the question. Please help me. Thank you.
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Old 04-15-2005, 01:08 AM   #2 (permalink)
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Oh dude, I know this is mad old, but still... Bad news man, bad news. Killed my buzz imediately.
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Old 04-15-2005, 05:01 AM   #3 (permalink)
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Google my friend!
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Old 04-15-2005, 09:34 AM   #4 (permalink)
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If your problem is in a math book then check the back, many books have answers to the study questions in the back.

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Old 04-15-2005, 09:36 AM   #5 (permalink)
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I am so confused .

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Old 04-15-2005, 01:02 PM   #6 (permalink)
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Math books usually only have the answers to the Odd questions in the back. If it is an even number problem, he's out of luck.
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Old 04-15-2005, 01:23 PM   #7 (permalink)
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Default Re: Help, Please!

Quote:
Originally posted by Megadeth2

To determine what each box actually contains, you may select one bohat from one box, without looking at the contents of that box.
Whats a bohat?
Is this some sort of American term I'm unaware of or just a typo?
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Old 04-15-2005, 01:29 PM   #8 (permalink)
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This should be easy. Lemme think about it. There are 6 unknowns - the six err.. hats.

There are six equations
- ALL boxes are labelled incorrectly (3 equations)
- You can figure out the identity of 1 hat (1 equations). One you pull out.
- 3 blue hats and 3 red hats (2 equations)

From 6 equations, and 6 unknowns, you can always find a unique solution assuming the equations are not redundant. In this case they are not as they all give you unique information.

Think about it. ..

EDIT: ma bad. didn't read question correctly. I rewrote it to make it accurate.
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Old 04-15-2005, 01:37 PM   #9 (permalink)
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Theres only 2 possible combinations you could have :

If all labels are wrong then :
box 1 : can contain either B + B OR R + B
box 2 : can contain either R + R OR R + B
box 3 : can contain either R + R oR B + B

IF B1 = B+B
B2 = R + R
THEN BOX 3 = R+B SO INCORRECT

IF B1 = B+B
B2 = R+B
B3 = R+R


IF B1 = R+B
B2 = R+R
B3 = B+B

IF B1 = R+B
B2 = R+B
B3 = R+B SO INCORRECT

Hope that at least narrows it down a bit for you. Tell me a bohat is & I'll work out the exact answer!
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Old 04-15-2005, 01:48 PM   #10 (permalink)
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Fine . I'll give u the full solution in the form of an algorithm. Before, I just wanted to show u that it is mathematically possible.

Box 1 must have a BLUE
Box 2 must have a RED
Box 3 is either (BB or RR)

Pick ONE from box 3 as per question. So you know whether it's BB or RR. Then you have 1 left of that color and 3 left of the other color

The "ONE" color left will go to either Box 1 or 2 depending on which color it is. One of the triplets will go to that box too. The other one will get the other 2 colors.

Easy
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