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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.

Sorry new to posting, was suppose to add a comment to my guess, will do it now.

The table is round. the 8 people sitting around the table sit in order of husband-wife-husband-wife-husband-wife-husband-wife.

The husband and wife from each couple is not allowed to sit together.

________H1 W2

W3 _______________H3

H4________________W4

________W1 H2

________H1 W2

W3_________________H4

H2________________W1

________W4 H3

There are the only two options. Husband 1 can only have Wife 1 sit opposite him or to the right as above (his lieft) if she sits to the left (his right) she will be sitting next to him. This applies to every other couple. I think where you might think there are more options is by changing seats around the table, but just by changing seats does not mean the order of who you are sitting next to changes. If you change seats eg. if H1 sets in the seat opposite from where he is sitting first hes still has to sit between W2 and W3, so in doing this it isn't a new seating order.

Thats how I read it any way. I might be wrong.

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How did you get so high?

The 1st there are 4 men who can sit

The 2nd there are 3 woman who can sit to fill conditions

3rd there are 2 men who can sit

4th there are 2 woman who can sit in the next gap

5th 1 posible

6th 1 posible

7th 1 posible

8th 1 posible

so 4x3x2x2 = 48

then swap men and woman around 48x2 = 96!

Edited by taliesin
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Seeing that brainden members are situated all over the world (me in nz) eight of us can't just meet and test this out around a table. Maybe it can be turned into a game where eight of us can be given a number and paired off with another member mimicking the husband wife combo, then if we number off the seats around the table and take turns at sitting around the table we can count how many times we sit next to someone new not being our partner (well in the case our online wife or husband). Maybe TwoaDay you can think of a way we could do this to show there are only two answers.

Thinking about it myself it may take a few times around the table, but each time we repeat the same position we have to eliminate that possiblity.

Just a thought and maybe it would be fun as well, unless of course everyone is in agreement with us that there are only two options :)

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Just wrote a script to calculate all the possibilities.. Guess What, it found 96.

Don't worry about the last column

Comment Seat1 Seat2 Seat3 Seat4 Seat5 Seat6 Seat7 Seat8 Itteration

1 M1 W2 M3 W1 M4 W3 M2 W4 3056

2 M1 W2 M3 W4 M2 W1 M4 W3 3098

3 M1 W2 M4 W1 M3 W4 M2 W3 3178

4 M1 W2 M4 W3 M2 W1 M3 W4 3194

5 M1 W3 M2 W1 M4 W2 M3 W4 3656

6 M1 W3 M2 W4 M3 W1 M4 W2 3698

7 M1 W3 M4 W1 M2 W4 M3 W2 3892

8 M1 W3 M4 W2 M3 W1 M2 W4 3920

9 M1 W4 M2 W1 M3 W2 M4 W3 4370

10 M1 W4 M2 W3 M4 W1 M3 W2 4424

11 M1 W4 M3 W1 M2 W3 M4 W2 4492

12 M1 W4 M3 W2 M4 W1 M2 W3 4520

13 M2 W1 M3 W2 M4 W3 M1 W4 7376

14 M2 W1 M3 W4 M1 W2 M4 W3 7418

15 M2 W1 M4 W2 M3 W4 M1 W3 7498

16 M2 W1 M4 W3 M1 W2 M3 W4 7514

17 M2 W3 M1 W2 M4 W1 M3 W4 8720

18 M2 W3 M1 W4 M3 W2 M4 W1 8740

19 M2 W3 M4 W1 M3 W2 M1 W4 8936

20 M2 W3 M4 W2 M1 W4 M3 W1 8956

21 M2 W4 M1 W2 M3 W1 M4 W3 9434

22 M2 W4 M1 W3 M4 W2 M3 W1 9466

23 M2 W4 M3 W1 M4 W2 M1 W3 9536

24 M2 W4 M3 W2 M1 W3 M4 W1 9556

25 M3 W1 M2 W3 M4 W2 M1 W4 12440

26 M3 W1 M2 W4 M1 W3 M4 W2 12460

27 M3 W1 M4 W2 M1 W3 M2 W4 12530

28 M3 W1 M4 W3 M2 W4 M1 W2 12562

29 M3 W2 M1 W3 M4 W1 M2 W4 13040

30 M3 W2 M1 W4 M2 W3 M4 W1 13060

31 M3 W2 M4 W1 M2 W3 M1 W4 13256

32 M3 W2 M4 W3 M1 W4 M2 W1 13276

33 M3 W4 M1 W2 M4 W3 M2 W1 14482

34 M3 W4 M1 W3 M2 W1 M4 W2 14498

35 M3 W4 M2 W1 M4 W3 M1 W2 14578

36 M3 W4 M2 W3 M1 W2 M4 W1 14620

37 M4 W1 M2 W3 M1 W4 M3 W2 17476

38 M4 W1 M2 W4 M3 W2 M1 W3 17504

39 M4 W1 M3 W2 M1 W4 M2 W3 17572

40 M4 W1 M3 W4 M2 W3 M1 W2 17626

41 M4 W2 M1 W3 M2 W4 M3 W1 18076

42 M4 W2 M1 W4 M3 W1 M2 W3 18104

43 M4 W2 M3 W1 M2 W4 M1 W3 18298

44 M4 W2 M3 W4 M1 W3 M2 W1 18340

45 M4 W3 M1 W2 M3 W4 M2 W1 18802

46 M4 W3 M1 W4 M2 W1 M3 W2 18818

47 M4 W3 M2 W1 M3 W4 M1 W2 18898

48 M4 W3 M2 W4 M1 W2 M3 W1 18940

49 W1 M2 W3 M1 W4 M3 W2 M4 21379

50 W1 M2 W3 M4 W2 M1 W4 M3 21421

51 W1 M2 W4 M1 W3 M4 W2 M3 21501

52 W1 M2 W4 M3 W2 M1 W3 M4 21517

53 W1 M3 W2 M1 W4 M2 W3 M4 21979

54 W1 M3 W2 M4 W3 M1 W4 M2 22021

55 W1 M3 W4 M1 W2 M4 W3 M2 22215

56 W1 M3 W4 M2 W3 M1 W2 M4 22243

57 W1 M4 W2 M1 W3 M2 W4 M3 22693

58 W1 M4 W2 M3 W4 M1 W3 M2 22747

59 W1 M4 W3 M1 W2 M3 W4 M2 22815

60 W1 M4 W3 M2 W4 M1 W2 M3 22843

61 W2 M1 W3 M2 W4 M3 W1 M4 25699

62 W2 M1 W3 M4 W1 M2 W4 M3 25741

63 W2 M1 W4 M2 W3 M4 W1 M3 25821

64 W2 M1 W4 M3 W1 M2 W3 M4 25837

65 W2 M3 W1 M2 W4 M1 W3 M4 27043

66 W2 M3 W1 M4 W3 M2 W4 M1 27063

67 W2 M3 W4 M1 W3 M2 W1 M4 27259

68 W2 M3 W4 M2 W1 M4 W3 M1 27279

69 W2 M4 W1 M2 W3 M1 W4 M3 27757

70 W2 M4 W1 M3 W4 M2 W3 M1 27789

71 W2 M4 W3 M1 W4 M2 W1 M3 27859

72 W2 M4 W3 M2 W1 M3 W4 M1 27879

73 W3 M1 W2 M3 W4 M2 W1 M4 30763

74 W3 M1 W2 M4 W1 M3 W4 M2 30783

75 W3 M1 W4 M2 W1 M3 W2 M4 30853

76 W3 M1 W4 M3 W2 M4 W1 M2 30885

77 W3 M2 W1 M3 W4 M1 W2 M4 31363

78 W3 M2 W1 M4 W2 M3 W4 M1 31383

79 W3 M2 W4 M1 W2 M3 W1 M4 31579

80 W3 M2 W4 M3 W1 M4 W2 M1 31599

81 W3 M4 W1 M2 W4 M3 W2 M1 32805

82 W3 M4 W1 M3 W2 M1 W4 M2 32821

83 W3 M4 W2 M1 W4 M3 W1 M2 32901

84 W3 M4 W2 M3 W1 M2 W4 M1 32943

85 W4 M1 W2 M3 W1 M4 W3 M2 35799

86 W4 M1 W2 M4 W3 M2 W1 M3 35827

87 W4 M1 W3 M2 W1 M4 W2 M3 35895

88 W4 M1 W3 M4 W2 M3 W1 M2 35949

89 W4 M2 W1 M3 W2 M4 W3 M1 36399

90 W4 M2 W1 M4 W3 M1 W2 M3 36427

91 W4 M2 W3 M1 W2 M4 W1 M3 36621

92 W4 M2 W3 M4 W1 M3 W2 M1 36663

93 W4 M3 W1 M2 W3 M4 W2 M1 37125

94 W4 M3 W1 M4 W2 M1 W3 M2 37141

95 W4 M3 W2 M1 W3 M4 W1 M2 37221

96 W4 M3 W2 M4 W1 M2 W3 M1 37263

Edited by taliesin
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Just wrote a script to calculate all the possibilities.. Guess What, it found 96.

Don't worry about the last column

Comment Seat1 Seat2 Seat3 Seat4 Seat5 Seat6 Seat7 Seat8 Itteration

1 M1 W2 M3 W1 M4 W3 M2 W4 3056

2 M1 W2 M3 W4 M2 W1 M4 W3 3098

3 M1 W2 M4 W1 M3 W4 M2 W3 3178

4 M1 W2 M4 W3 M2 W1 M3 W4 3194

5 M1 W3 M2 W1 M4 W2 M3 W4 3656

6 M1 W3 M2 W4 M3 W1 M4 W2 3698

7 M1 W3 M4 W1 M2 W4 M3 W2 3892

8 M1 W3 M4 W2 M3 W1 M2 W4 3920

9 M1 W4 M2 W1 M3 W2 M4 W3 4370

10 M1 W4 M2 W3 M4 W1 M3 W2 4424

11 M1 W4 M3 W1 M2 W3 M4 W2 4492

12 M1 W4 M3 W2 M4 W1 M2 W3 4520

13 M2 W1 M3 W2 M4 W3 M1 W4 7376

14 M2 W1 M3 W4 M1 W2 M4 W3 7418

15 M2 W1 M4 W2 M3 W4 M1 W3 7498

16 M2 W1 M4 W3 M1 W2 M3 W4 7514

17 M2 W3 M1 W2 M4 W1 M3 W4 8720

18 M2 W3 M1 W4 M3 W2 M4 W1 8740

19 M2 W3 M4 W1 M3 W2 M1 W4 8936

20 M2 W3 M4 W2 M1 W4 M3 W1 8956

21 M2 W4 M1 W2 M3 W1 M4 W3 9434

22 M2 W4 M1 W3 M4 W2 M3 W1 9466

23 M2 W4 M3 W1 M4 W2 M1 W3 9536

24 M2 W4 M3 W2 M1 W3 M4 W1 9556

25 M3 W1 M2 W3 M4 W2 M1 W4 12440

26 M3 W1 M2 W4 M1 W3 M4 W2 12460

27 M3 W1 M4 W2 M1 W3 M2 W4 12530

28 M3 W1 M4 W3 M2 W4 M1 W2 12562

29 M3 W2 M1 W3 M4 W1 M2 W4 13040

30 M3 W2 M1 W4 M2 W3 M4 W1 13060

31 M3 W2 M4 W1 M2 W3 M1 W4 13256

32 M3 W2 M4 W3 M1 W4 M2 W1 13276

33 M3 W4 M1 W2 M4 W3 M2 W1 14482

34 M3 W4 M1 W3 M2 W1 M4 W2 14498

35 M3 W4 M2 W1 M4 W3 M1 W2 14578

36 M3 W4 M2 W3 M1 W2 M4 W1 14620

37 M4 W1 M2 W3 M1 W4 M3 W2 17476

38 M4 W1 M2 W4 M3 W2 M1 W3 17504

39 M4 W1 M3 W2 M1 W4 M2 W3 17572

40 M4 W1 M3 W4 M2 W3 M1 W2 17626

41 M4 W2 M1 W3 M2 W4 M3 W1 18076

42 M4 W2 M1 W4 M3 W1 M2 W3 18104

43 M4 W2 M3 W1 M2 W4 M1 W3 18298

44 M4 W2 M3 W4 M1 W3 M2 W1 18340

45 M4 W3 M1 W2 M3 W4 M2 W1 18802

46 M4 W3 M1 W4 M2 W1 M3 W2 18818

47 M4 W3 M2 W1 M3 W4 M1 W2 18898

48 M4 W3 M2 W4 M1 W2 M3 W1 18940

49 W1 M2 W3 M1 W4 M3 W2 M4 21379

50 W1 M2 W3 M4 W2 M1 W4 M3 21421

51 W1 M2 W4 M1 W3 M4 W2 M3 21501

52 W1 M2 W4 M3 W2 M1 W3 M4 21517

53 W1 M3 W2 M1 W4 M2 W3 M4 21979

54 W1 M3 W2 M4 W3 M1 W4 M2 22021

55 W1 M3 W4 M1 W2 M4 W3 M2 22215

56 W1 M3 W4 M2 W3 M1 W2 M4 22243

57 W1 M4 W2 M1 W3 M2 W4 M3 22693

58 W1 M4 W2 M3 W4 M1 W3 M2 22747

59 W1 M4 W3 M1 W2 M3 W4 M2 22815

60 W1 M4 W3 M2 W4 M1 W2 M3 22843

61 W2 M1 W3 M2 W4 M3 W1 M4 25699

62 W2 M1 W3 M4 W1 M2 W4 M3 25741

63 W2 M1 W4 M2 W3 M4 W1 M3 25821

64 W2 M1 W4 M3 W1 M2 W3 M4 25837

65 W2 M3 W1 M2 W4 M1 W3 M4 27043

66 W2 M3 W1 M4 W3 M2 W4 M1 27063

67 W2 M3 W4 M1 W3 M2 W1 M4 27259

68 W2 M3 W4 M2 W1 M4 W3 M1 27279

69 W2 M4 W1 M2 W3 M1 W4 M3 27757

70 W2 M4 W1 M3 W4 M2 W3 M1 27789

71 W2 M4 W3 M1 W4 M2 W1 M3 27859

72 W2 M4 W3 M2 W1 M3 W4 M1 27879

73 W3 M1 W2 M3 W4 M2 W1 M4 30763

74 W3 M1 W2 M4 W1 M3 W4 M2 30783

75 W3 M1 W4 M2 W1 M3 W2 M4 30853

76 W3 M1 W4 M3 W2 M4 W1 M2 30885

77 W3 M2 W1 M3 W4 M1 W2 M4 31363

78 W3 M2 W1 M4 W2 M3 W4 M1 31383

79 W3 M2 W4 M1 W2 M3 W1 M4 31579

80 W3 M2 W4 M3 W1 M4 W2 M1 31599

81 W3 M4 W1 M2 W4 M3 W2 M1 32805

82 W3 M4 W1 M3 W2 M1 W4 M2 32821

83 W3 M4 W2 M1 W4 M3 W1 M2 32901

84 W3 M4 W2 M3 W1 M2 W4 M1 32943

85 W4 M1 W2 M3 W1 M4 W3 M2 35799

86 W4 M1 W2 M4 W3 M2 W1 M3 35827

87 W4 M1 W3 M2 W1 M4 W2 M3 35895

88 W4 M1 W3 M4 W2 M3 W1 M2 35949

89 W4 M2 W1 M3 W2 M4 W3 M1 36399

90 W4 M2 W1 M4 W3 M1 W2 M3 36427

91 W4 M2 W3 M1 W2 M4 W1 M3 36621

92 W4 M2 W3 M4 W1 M3 W2 M1 36663

93 W4 M3 W1 M2 W3 M4 W2 M1 37125

94 W4 M3 W1 M4 W2 M1 W3 M2 37141

95 W4 M3 W2 M1 W3 M4 W1 M2 37221

96 W4 M3 W2 M4 W1 M2 W3 M1 37263

1 M1 W2 M3 W1 M4 W3 M2 W4 3056

21 M2 W4 M1 W2 M3 W1 M4 W3 9434

They are seated around a round table. I am not going to go through all the 96 combinations (yet) but will point out two to make a point.

If you were to place option number 1 around a round table and option number 21 around a round table, everyone will be sitting next to the same people, in the same order.

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1 M1 W2 M3 W1 M4 W3 M2 W4 3056

21 M2 W4 M1 W2 M3 W1 M4 W3 9434

They are seated around a round table. I am not going to go through all the 96 combinations (yet) but will point out two to make a point.

If you were to place option number 1 around a round table and option number 21 around a round table, everyone will be sitting next to the same people, in the same order.

But they are in different seats ,so it is a different permintation

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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?

It doesn't ask for seat placement. If they did, then I would have to agree with you.

Lets take option number 1 and 21, the 8 people are seated exactly the same way, just in different seats.

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The question is ambiguous as to whether everyone shifting one seat to the left (for instance) is a distinct "way" of seating. It's a much more interesting problem if you assume it is not, so that's what I've looked at. Here's how I approached it.

Start by keeping the men seating order constant - M1 W? M2 W? M3 W? M4 W? for convenience. Each of those W spots could contain one of two women - M1 W(3,4) M2 W(1,4) M3 W(1,2) M4 W(2,3). Because of the way these are linked, this allows only 2 possibilities - M1 W3 M2 W4 M3 W1 M4 W2 and M1 W4 M2 W1 M3 W1 M4 W2. These are two distinct possibilities.

You can then rearrange the order of the men sitting. The problem arising here is that you want to avoid configurations that are just rotations of other ones. To watch for this, it's easiest to always start with M1, and rearrange the others from there:

M1 M2 M3 M4

M1 M2 M4 M3

M1 M3 M2 M4

M1 M3 M4 M2

M1 M4 M2 M3

M1 M4 M3 M2

Again, these are all distinct possibilities. Combining that with 2 ways each of arranging the women, you get a total of 12 possibilities:

1 M1 W2 M3 W1 M4 W3 M2 W4 3056

2 M1 W2 M3 W4 M2 W1 M4 W3 3098

3 M1 W2 M4 W1 M3 W4 M2 W3 3178

4 M1 W2 M4 W3 M2 W1 M3 W4 3194

5 M1 W3 M2 W1 M4 W2 M3 W4 3656

6 M1 W3 M2 W4 M3 W1 M4 W2 3698

7 M1 W3 M4 W1 M2 W4 M3 W2 3892

8 M1 W3 M4 W2 M3 W1 M2 W4 3920

9 M1 W4 M2 W1 M3 W2 M4 W3 4370

10 M1 W4 M2 W3 M4 W1 M3 W2 4424

11 M1 W4 M3 W1 M2 W3 M4 W2 4492

12 M1 W4 M3 W2 M4 W1 M2 W3 4520

These are all distinct from each other. If you are interpreting "how many ways" differently from this, please explain.

Man oh man is work awesome.

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theres only @?$%^n 2

Please show me how any two of those are the same. By "the same," I mean: take the place of M1 - if everybody is in the same position from your perspective, it is "the same."

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The question is ambiguous as to whether everyone shifting one seat to the left (for instance) is a distinct "way" of seating. It's a much more interesting problem if you assume it is not, so that's what I've looked at. Here's how I approached it.

Start by keeping the men seating order constant - M1 W? M2 W? M3 W? M4 W? for convenience. Each of those W spots could contain one of two women - M1 W(3,4) M2 W(1,4) M3 W(1,2) M4 W(2,3). Because of the way these are linked, this allows only 2 possibilities - M1 W3 M2 W4 M3 W1 M4 W2 and M1 W4 M2 W1 M3 W1 M4 W2. These are two distinct possibilities.

You can then rearrange the order of the men sitting. The problem arising here is that you want to avoid configurations that are just rotations of other ones. To watch for this, it's easiest to always start with M1, and rearrange the others from there:

M1 M2 M3 M4

M1 M2 M4 M3

M1 M3 M2 M4

M1 M3 M4 M2

M1 M4 M2 M3

M1 M4 M3 M2

Again, these are all distinct possibilities. Combining that with 2 ways each of arranging the women, you get a total of 12 possibilities:

1 M1 W2 M3 W1 M4 W3 M2 W4 3056

2 M1 W2 M3 W4 M2 W1 M4 W3 3098

3 M1 W2 M4 W1 M3 W4 M2 W3 3178

4 M1 W2 M4 W3 M2 W1 M3 W4 3194

5 M1 W3 M2 W1 M4 W2 M3 W4 3656

6 M1 W3 M2 W4 M3 W1 M4 W2 3698

7 M1 W3 M4 W1 M2 W4 M3 W2 3892

8 M1 W3 M4 W2 M3 W1 M2 W4 3920

9 M1 W4 M2 W1 M3 W2 M4 W3 4370

10 M1 W4 M2 W3 M4 W1 M3 W2 4424

11 M1 W4 M3 W1 M2 W3 M4 W2 4492

12 M1 W4 M3 W2 M4 W1 M2 W3 4520

These are all distinct from each other. If you are interpreting "how many ways" differently from this, please explain.

Man oh man is work awesome.

um....wow.....

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no i dont have time

It shouldn't take too long. If there are only two, then you can just find which two are correct, and then show how another one is a duplicate of those. Just show they any two of them are the same, and you will have proved me wrong.

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i reasearched it and there are definately only two answers

it will be really, REALLY hard for anyone to change my mind or prove my wrong (and thats probably because its impossible, i know im right)

and again GJ tearz

might i suggest you post a link to your source and then we can take the time ourselves to see the reasoning for only 2, i am seeing that 12 is a reasonable answer and then if the first person can sit in any of 8 different starting chairs there should be around 96 possibilities

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