Question by Pimpinme123: math help please!?
a math teacher takes a group of kids who hasnt been doing HW into a room. In the room is a large circular table with enough chairs for all the kids. the teacher has a stack of worksheets and if you are handed the WS, you must go to a diff room to finish it.The 1st WS is given to the kid in chair 1. then the techer will skip the kid in chair 2 and give the WS to the kid in chair 3, who will follow the 1st kid across the hall to work on the assignment. the process contineus, skipping 1 kid and sending the enxt one off all the way around the table. When the teacher gets back to the begining of the table he starts the cycle again. (meaning he removes the last or next to last kid at the “end” of the table, skip the next kid, and remove whoever follows. he doesnt start over with the 1st kid again) The last kid gets an A+ and no HW for the year. the teacher tells everyone to get seated, and u have to decide where to sit in order to be the last kid.
how do u come up with a quick rule that can be used to know where to sit no matter how many students there are?
a. where could you sit if there was 21 kids?
b. 75 kids?
c. 120 kids?
d. whats the rule for “n” students?
use the answer for question (c) as ur short answer. explain your approah to solve this probelm and your rule to determine where to sit.
PLEASE help! thank you!
Best answer:
Answer by Kia
This is a very interesting puzzle with a relatively simple solution. If the number of the kids were a power of 2, you have to sit at the very end. The reason for that is that everytime around the table, exactly half the student go away, and what’s left is also a power of 2, and the person at the end will will always be at an even position. Let me give you an example. If there are 8 students and let’s say that the chairs are numbered, the students will leave in the following order:
1, 3, 5, 7, 2, 6, 4 and the last person is number 8.
Let’s do the same with 16 students:
1, 3, 5, 7, 9, 11, 13, 15, 2, 6, 10, 14, 4, 12, 8 and the last person is number 16
Now what do you do when the number of students is not a power of 2. Well, all you have to do is find out where you have to be when the number of students remaining has reached a power of 8. Here is how it works:
Let n be the number of students
Let p be the highest power of 2 less than n
You want to be in seat (n – p) * 2
Let’s try an example. Let’s say that there are 11 students, so n = 11, p = 8, and you want to be in seat (11-8) * 2 = 6
So let’s see, 1, 3, 5, 7, 9, 11, 4, 8, 2, 10 and the last person is in seat 6
Let’s do another test. 27 students. In this case, n= 27, p = 16, and you want to be in seat (27-16) * 2 = 22
So let’s see, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 4, 8, 12, 16, 20, 24, 2, 10, 18, 26, 14, 6 and the last person is in seat 22
In summary, if the number of students is a power of 2, you want to be in the last chair, other than that, you want to be in chair (n-p)*2
So for 21 kids, n = 21, p = 16, and you want to be in chair:
(21-16)*2 = 10
For 75 kids, n = 75, p = 64, and you want to be in chair:
(75-64)*2 = 22
For 120 kids, n = 120, p = 64, and you want to be in chair:
(120-64)*2 = 112
I hope this helped
Kia
Add your own answer in the comments!
Recent Comments