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Eleven boys and girls wait to take their seats in the same
row in a movie theater. There are exactly 11 seats in the row.
They decided that after the first person sits down, the next
person has to sit next to the first. The third sits next to
one of the first two and so on until all eleven are seated.
In other words, no person can take a seat that separates
him/her from at least one other person.
How many different ways can this be accomplished? Note that
the first person can choose any of the 11 seats.
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Answer / guest
There are 1024 different ways.
This is the type of Brain Teaser that can be solved using
the method of induction.
If there is just a one person and one seat, that person has
only one option.
If there are two persons and two seats, it can be
accomplished in 2 different ways.
If there are three persons and three seats, it can be
accomplished in 4 different ways. Remember that no person
can take a seat that separates him/her from at least one
other person.
Similarly, four persons and four seats produce 8 different
ways. And five persons with five seats produce 16 different
ways.
It can be seen that with each additional person and seat,
the different ways increase by the power of two. For six
persons with six seats, there are 32 different ways.
For any number N, the different possible ways are 2(N-1)
Thus, for 11 persons and 11 seats, total different ways are
210 i.e. 1024
| Is This Answer Correct ? | 3 Yes | 2 No |
Answer / nikitha
for starting with one person there will be 4 ways n for 11
persons it will be 44 ways
| Is This Answer Correct ? | 0 Yes | 0 No |
Answer / lopamudra
answer will be 1
bcs there are same no. of guys n seats....and no can be
separate from the other person next to him/her
| Is This Answer Correct ? | 0 Yes | 0 No |
Answer / puchi mukhujje (:-p)
i think you're trying to say that each person is previously numbered from 1 to 11.
the first person can choose his seat between the two corner seats and 11 other seats.if he chooses one of the corner seats which he can do in 2 ways,then because there is only one vacant seat beside him, the 2nd person will have to sit on that seat and so on.
now let us mark the middle seats from 1 to 9.now if he picks the nth seat,you notice,after they're all seated, that on both sides of the 1st person people are seated with their numbers in ascending order.when 1 chooses the nth seat, the no. of ways in which they can be seated becomes 10Cn. 1 can choose any seat from 1 to 9.
so the total no. of ways is 2^10-2+2=2^10 (ans.)
| Is This Answer Correct ? | 0 Yes | 0 No |
Answer / nikitha
I think it can be done only in 2 ways.why bcz if 1st person
takes any other seat other than 1st and last, then the
continuation may be lost.
| Is This Answer Correct ? | 0 Yes | 1 No |
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