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abc
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6 men with their wives ( total of 12 ) in how many ways can they sit in a circular table but no man sits beside his wife ?
needs smart people
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abc
needs smart people
cheers
abc
mattmns said:Question: If 6 men sit next to each other, and 6 women sit next to each other (at the same time) Is this counted as 1 possibility, or 12?
But the men and women ARE numbered right? So permuting (or is it permutating?) the men will give a different arrangement and permut(at)ing the women will as well.Rogerio said:Just 1 possibility. Remember it is a circular table.
Gokul43201 said:It's 1 arrangement (not 12). We are not told that the seats are numbered, so must assume they are identical.
Gokul43201 said:I believe the number will be larger than 500,000.
abc said:6 men with their wives ( total of 12 ) in how many ways can they sit in a circular table but no man sits beside his wife ?
needs smart people
cheers
abc
hemmul said:i got 12!-4*6!
if it is true - i'll explain the solution...
Rogerio said:Unfortunately it's false: it can't be more than 11!
b0mb0nika said:...so there are
11! -5! x 2
ways to arrange the people such that no man sits beside his wife
i believe that is the answer
Diana
I don't believe you. There is much involved in subtracting the possibilities that 1, 2, 3, 4, or 5 couples could be seated together and a lot of room for error. Let's see your work.b0mb0nika said:i did get the same answer as you after doing it like that
Rogerio said:12,771,840
Number of people Solutions
4 2 (1)
6 32 (16)
8 1488 (744)
10 112512 (56256)
12 12771840 (6385920)
// round_table.c
// solves the puzzle: how many ways can 6 couples sit around a round table without any man sitting next to his wife?
// ceptimus: 2005-01-22
#include "stdio.h"
// the size of the table (number of chairs, and number of people)
#define PLACES 12
int chair[PLACES]; // 0 indicates that a chair is empty, or 1 to PLACES says which person is occupying it
unsigned long solutions; // counts the number of solutions found
void seat(int person) // sit [person] somewhere (if possible) and move onto next person
{
int position;
int places;
if (person == 2)
places = 1 + PLACES / 2; // only try the first wife on one side, or opposite her husband
else
places = PLACES; // try all the other people in each available place
if ((chair[PLACES / 2] == 2) && (person == 3)) // if the first wife is seated opposite her husband
places = PLACES / 2; // only try the second husband on one side of the table
// above lines just eliminate mirror image solutions. To count such solutions, remove // from following line
// places = PLACES;
for (position = 1; position < places; position++)
{
if (!chair[position]) // if the chair is empty
{
if (person % 2) // if person is an odd number (i.e. a man)
chair[position] = person; // seat him
else // a woman
if
(
(chair[(position - 1) % PLACES] != (person - 1)) && // her husband isn't in the chair to the left
(chair[(position + 1) % PLACES] != (person - 1)) // or in the position to the right
)
chair[position] = person; // seat her
if (chair[position]) // if the person has been seated
{
if (person == PLACES) // if all the people have been seated
solutions++; // we've found and extra solution
else
seat(person + 1); // try to seat the next person
chair[position] = 0; // make the person stand up again, so we can search for further solutions
}
}
}
}
int main(int argc, char* argv[])
{
int i;
for (i = 0; i < PLACES; i++)
chair[i] = 0; // all chairs are empty
solutions = 0L; // no solutions found yet
chair[0] = 1; // sit the first man in the first chair
seat(2); // sit his wife somewhere (and then try to seat all the remaining people)
printf("%lu solutions found for seating %u people\n", solutions, PLACES);
return 0;
}
There are 720 possible seating arrangements for 6 men and their wives, assuming that each couple must sit together and the men and women alternate in the seating arrangement.
No, the men and their wives must alternate in the seating arrangement. This means that a man cannot sit next to his wife and a woman cannot sit next to her husband.
Yes, in order to follow the alternating pattern, the men and their wives should be seated in the order of man, woman, man, woman, man, woman.
Yes, as long as they are alternating with the men, the wives can sit in any order within the alternating pattern.
The number of possible seating arrangements will differ depending on the number of men and their wives. For example, if there are 8 people (4 men and 4 women), there will be 4! (24) possible seating arrangements. If there are 10 people (5 men and 5 women), there will be 5! (120) possible seating arrangements.