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Six people are sitting around a circular table, and each person has either blue eyes or green eyes. Let x be the number of people sitting next to at least one blue-eyed person, and let y be the number of people sitting next to at least one green-eyed person. How many possible ordered pairs (x,y) are there? (For example, (x,y) = (6,0) if all six people have blue eyes, since all six people are sitting next to a blue-eyed person, and zero people are sitting next to a green-eyed person.)

 May 29, 2020
 #1
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off the top of my head...

0 to 6 for blue and 0 to 6 for green = 49 

that is assuming that a person can have one green eye and one blue eye. (probably not what was intended   wink)

 May 29, 2020
 #2
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otherwise try looking at each scenario seperately

 

0 blue, 6 green

1 blue, 5 green

etc

Some are easy some  will be hard.

Show us what you can do on your own.

 

 

No one else do this problem for guest. Thanks.

 May 29, 2020
 #4
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I need help here to

 May 30, 2020
 #5
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@melody it's more difficult then you stated in problem 2. I'm not sure about this either, but here's nine possible (x,y)'s:

1. (0, 6)

2. (2, 6)

3. (4, 6)

4. (3, 5)

5. (5, 5)

6. (6, 4)

7. (5, 3)

8. (6, 2)

9. (6, 0)

NOTE: 1 is not a possible value of x or y

 May 30, 2020
 #6
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Wait I found 2 more.

1. (6, 0)

2. (6, 2)

3. (6, 3)

4. (6, 4)

5. (5, 3)

6. (5, 5)

7. (4, 6)

8. (3, 5)

9. (3, 6)

10. (2, 6)

11. (0, 6)

Guest May 30, 2020
 #7
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You over counted the answer is 10

Guest May 30, 2020
 #8
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I did not say it was easy, I said parts  of it were easy and I gave a start point

 

this is exactly what i said.

 

Try looking at each scenario separately,

0 blue, 6 green

1 blue, 5 green

etc

Some are easy some  will be hard.

Show us what you can do on your own.

 

 

Did guest show what he could do on his own?

OR did you just race in and give him an answer?  (which may or may not be correct)

 

I should not sound too negative about it, if the question inspired you to practice or learn something then your effort is of value (to you)

Your answer only has cheat value to the asker however.

Melody  May 31, 2020
edited by Melody  May 31, 2020

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