Mitch wants to decide who is most fit to date his daughter. They are all fine yo
ID: 3119984 • Letter: M
Question
Mitch wants to decide who is most fit to date his daughter. They are all fine young people but Mitch wanted his daughter to be with someone who is clever. When all her suitors were seated around his large round Ikea table. Mitch pointed to one kid and said. "You stay". The next wasn't so lucky, "You leave", said Mitch. To the third, he said, "You stay". He continued around the table in this fashion until there was only one young person left. This clever (or lucky) person was allowed to date Mitch's daughter. What position would you tell a prospective suitor to sit in if there were 14 chairs at the table? Explain your method. (You may want to complete the t chart.) What position would you sit in if there were 100 chairs? Write an algebraic model that will allow you to predict the winning position for any number of chairs.Explanation / Answer
For the first round, all even number (2k) chaired people will be eliminated and all odd numbered chair (2k+1) people will stay.
That is, for the 14 chairs case: 1,3,5,7,9,11,13 will stay after 1 round and 2,4,6,8,10,12,14 will be eliminated.
Now in the second round all the people whose chair numbers are of the form 4k+1 will stay the others whose chair numbers aer of the form 4k+3 will leave.
So 1,5,9,13 will stay.
After this, the last person to be selected for staying was 13. Hence 1 and 9 will be elimiated and 5 and 13 will stay. After 13, the next seat numbered 5 will be eliminated and only seat numbered 13 suitor will stay and will get to marry Mitch's daughter.
For 100 chairs, all odd numbered people will stay in round 1 and even numbered people will be eliminated. Remaining chairs = 100-50=50
1,3,5,7,...97,99 are left
Starting from 1 again, all the numbers of the form 4k+1 will stay and the rest will leave. TOtal of 50-25 people stay and they are,
1,5,9,...97
Now since 99 left, 1 will stay and similarly all the numbers of the form 8k+1 will stay. Thus of the total 25 members 12 will leave.
1,9,17....81,89,97 will stay (13 seats in total)
Since odd numbered of seats were left in the last round, and 97 was the last person who stayed, 1 wil leave, similarly 17,33 wil leave. So only those numbers of the form 16k+9 will stay.
9,25,...89 (out of 13 people 7 have left so 6 seats are left.
9,25,41,57,73,89,
since 89 stayed, 9, 41,73 leave.
Now we have 25,57,89 will stay .
Since 89 stayed, 25 leaves, 57 stays and 89 leaves.
Thus for 100 seats person sitting on seat numbered 57 stays.