@nisroms I think it will be 3x11!. Let the square table be PQRS, and take one of the people as A. Now, suppose A is sitting on side PQ. There are 3 distinct places where A can sit. For each of these positions, the other 11 people can be arranged in 11! ways. Hence total arrangements is 3x11!
I am considering the 4 sides to be equivalent. So any arrangement where A is sitting on sides RS/QR/SP can be obtained by simply rotating some arrangement we obtained in the case above (where A is on side PQ).
This is analogous to sitting around a circular table, where you fix A in one position and arrange the other guys in 11! ways. All other arrangements, with A in a different position, can be obtained by rotation of some previously considered arrangement=>we get 1x11! = 11! arrangements. But in our square waala case, there are 3 different spots that A can take, so 3x11!
Using the same logic, suppose the table was a rectangle with 2 chairs on one side and 4 chairs on the other, 12 chairs in total. Answer in this case should be 6x11!
Tera logic kuch samaj nhi aaya thk se...thoda vistaar mein bta...xplain the line in italics..
@ankita14 Didn't get you there. 4 people on a square table will only have 1 guy per side, so isme kya hi distinguish karenge.. There is only 1 unique position for our reference point, and all others can be obtained via rotation. It will be 1x3!, like in a circle.
But I guess you meant 4 people per side of the table. Suppose the positions are A,B,C and D along any one side, in this particular order. Did you mean that A and D should not be distinguished between? :/
@ankita14 Didn't get you there. 4 people on a square table will only have 1 guy per side, so isme kya hi distinguish karenge.. There is only 1 unique position for our reference point, and all others can be obtained via rotation. It will be 1x3!, like in a circle.
But I guess you meant 4 people per side of the table. Suppose the positions are A,B,C and D along any one side, in this particular order. Did you mean that A and D should not be distinguished between? :/
I meant in the 12 people case there ARE 4 people on each side, I was thinking that there were 3 people on each side which is why I could not understand why would you distinguish between the corner positions.
@ankita14 Didn't get you there. 4 people on a square table will only have 1 guy per side, so isme kya hi distinguish karenge.. There is only 1 unique position for our reference point, and all others can be obtained via rotation. It will be 1x3!, like in a circle.
But I guess you meant 4 people per side of the table. Suppose the positions are A,B,C and D along any one side, in this particular order. Did you mean that A and D should not be distinguished between? :/
Oh no wait you don't put the chairs at the corners do you? I have become stooopid!
@ankita14 Didn't get you there. 4 people on a square table will only have 1 guy per side, so isme kya hi distinguish karenge.. There is only 1 unique position for our reference point, and all others can be obtained via rotation. It will be 1x3!, like in a circle.
But I guess you meant 4 people per side of the table. Suppose the positions are A,B,C and D along any one side, in this particular order. Did you mean that A and D should not be distinguished between? :/
@RoadKill bhai...how can you extend this logic to a rectangle....i did not get this point....when we are talking about a square....we can extend the logic of circle bcoz it is symmetrical....the only diff is 3 seats per side...so A chooses out of those 3...after that it becomes a linear arrangement bcoz it is symmetrical....elucidate...!!!
@RoadKill bhai...how can you extend this logic to a rectangle....i did not get this point....when we are talking about a square....we can extend the logic of circle bcoz it is symmetrical....the only diff is 3 seats per side...so A chooses out of those 3...after that it becomes a linear arrangement bcoz it is symmetrical....elucidate...!!!
In a rectangle, according to roadkill's example there would be 6 unique positions A could take hence 6*11!
In a rectangle, according to roadkill's example there would be 6 unique positions A could take hence 6*11!
Vo samajh aa gaya....par Rectangle is not symmetrical...so even after A takes one of these position....it still can't be considered linear arrangement...that's my doubt...@RoadKill
@RoadKill bhai...how can you extend this logic to a rectangle....i did not get this point....when we are talking about a square....we can extend the logic of circle bcoz it is symmetrical....the only diff is 3 seats per side...so A chooses out of those 3...after that it becomes a linear arrangement bcoz it is symmetrical....elucidate...!!!
Dekho aise...rectangle is also symmetrical along the diagonal.....so there are 6 seats on one side and 6 on the other...toh A has 6 distinct places...and baaki kahi bhi rakhoge toh rotate karke mil jayega...symmetry ka dhyaan rakho aise questions mein...
Vo samajh aa gaya....par Rectangle is not symmetrical...so even after A takes one of these position....it still can't be considered linear arrangement...that's my doubt...@RoadKill
It is symmetrical about the diagonal na :/ so 6 positions are the exact replica of the remaining 6.
*hurt* :nono: