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TwoaDay

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Four couples enter a restaurant. How many ways can they be seated at a round table so that the men and women alternate and no husband and wife sit next to each other?

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Well crud. Just because I look like I'm good at math doesn't mean I am (right Yoruichi-san?)

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two, if husbands cannot sit next to their wives then they can only sit accross from them in two spots

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but you can reflect seating arrangements

and also, there's three women a man man can sit next to

so 3 combinations of the two women sitting next to a man

and 6 if you reflect the seating

but i don't know what the answer is

Edited by lemonymelon

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6

If we call the women w1, w2, w3 and w4 and take any one man M. Presume w4 is the wife of the man and therefore cannot sit beside him. The combinations are as follows:

w1 M w2

w2 M w1

w1 M w3

w3 M w1

w2 M w3

w3 M w2

So six combinations?

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just to claryify there are 4 men and 4 women

they have to be seated alternating mwmwmwmw

and the man and women in each couple cannot be sitting next to each other

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nooo thats worse than before

How is 12 worse than my guess of 6? Ive figured out there are at least 12...so if anything its better than my other guess!!

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These are the 12 combinations I have so far. Maybe I mis-read the question?

If it has m before it its the man, if it doesn't its the women. I couldnt show the example in circles, so have put them in a line, same thing though - just imagine it in a circle!

m4 3 m2 1 m3 4 m1 2

m4 3 m1 4 m2 1 m3 2

m4 3 m2 4 m1 2 m3 1

m4 3 m1 2 m3 4 m2 1

m4 2 m1 4 m3 1 m2 3

m4 2 m3 1 m2 4 m1 3

m4 2 m1 3 m2 4 m3 1

m4 2 m3 4 m1 3 m2 1

m4 1 m2 3 m1 4 m3 2

m4 1 m3 4 m1 3 m2 2

m4 1 m2 4 m3 2 m1 3

m4 1 m3 4 m1 2 m2 3

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well it seems that you are right

i was disagreeing because the book i got this from said there were only 2

i never really checked for more but i cant find anything wrong with your answers

thank you for correcting the book, and good job

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ok, i finally realized why there are only two answers

beacause this is a circular table, there is no first or last person. all of the variations posted other that the two are all just starting with different people, and yes i am pretty very sure about this.

B)) B)) :DB)):ph34r: :ph34r:

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ok, i finally realized why there are only two answers

beacause this is a circular table, there is no first or last person. all of the variations posted other that the two are all just starting with different people, and yes i am pretty very sure about this.

B)) B)) :DB)):ph34r: :ph34r:

If u imagine all my answers in circular form, there are 12 different variations. I don't understand what you are trying to say is wrong with it - can you be more specific?

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There are only two ways. Alternating with husband and wife opposite each other and beside each other.

So my answer is 2.

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name='starfish' date='Jul 27 2008, 03:09 PM' post='53712']

These are the 12 combinations I have so far. Maybe I mis-read the question?

If it has m before it its the man, if it doesn't its the women. I couldnt show the example in circles, so have put them in a line, same thing though - just imagine it in a circle!

m4 w3 m2 w1 m3 w4 m1 w2 this

m4 w3 m1 w4 m2 w1 m3 w2 this

m4 w3 m2 w4 m1 w2 m3 w1

m4 w3 m1 w2 m3 w4 m2 w1

m4 w2 m1 w4 m3 w1 m2 w3 and this are the same

m4 w2 m3 w1 m2 w4 m1 w3 and this are the same

m4 w2 m1 w3 m2 w4 m3 w1

m4 w2 m3 w4 m1 w3 m2 w1

m4 w1 m2 w3 m1 w4 m3 w2

m4 w1 m3 w4 m1 w3 m2 w2 this doesent work

m4 w1 m2 w4 m3 w2 m1 w3

m4 w1 m3 w4 m1 w2 m2 w3 this dosent work

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