Thread: End of the year calculus challenge

Alright, my teacher has given us an end of the year calculus challenge problem that he would like to see if anyone understands.

The problem is:
"In order to pass calculus class, the student must sit in the right seat, give me a formula or equation that shows the correct seat for any possible size of class" (In this case of this problem, ONE person may pass the calculus class)

(we have 8 people in my calculus class....yes i know, small school)
He put us in a circle and then showed us the pattern.

First the 1st, 3rd, 5th, and 7th people in the circle (STARTING AT A COUNTER CLOCKWISE ROTATION) were removed from the possibilities, then he removed the 2nd and 6th people the next time he repeated the circle, afterwards he removed the 3rd which left the 8th person remaining.

I've been able to get the follow statistics (number of people in the circle / "winning seat")

2 - 2
3 - 2
4 -4
5 - 2
6 - 4
7 - 6
8 - 8
9 -2
10 -4
11 - 6
12 - 8
13 - 10
14-12
15-14
16 - 16
17 - 2
18 - 4
19 - 6
20 - 8
21 - 10
22 - 12
23 - 14
24 -16
25 - 18

and it continues in a pattern like that, does anyone have any idea how i would go about finding the equation(s) to solve this?

Is my initial reaction...

Do you mean that there's n seats in the class and in order to pass the student must sit in the right seat?

Can you explain this better? Or at least explain how you got your answers so we (or maybe its just me...) can figure out whats going on.

Originally Posted by Deadstar

Is my initial reaction...

Do you mean that there's n seats in the class and in order to pass the student must sit in the right seat?

Can you explain this better? Or at least explain how you got your answers so we (or maybe its just me...) can figure out whats going on.

okay, theres a said circle of people...and the person who's last standing at the end of each one is the person who "passes" or "wins" the class.

So the first person is always out and then you switch off between the remaining people..

The best way i think i can explain it is to have you draw 8 people in a circle (use circles, dots, whatever) and X out the person who is elminated each time until there is only one left. Each time it rotates who stays and leaves..... In, Out, In, Out, etc until there is one person standing. I need to find a formula for the position of the last person standing for that pattern.

Epic, now i get it. Right ill have a look at it but if your stats are right it might just be easier to find a formula for them.

Originally Posted by Deadstar

Epic, now i get it. Right ill have a look at it but if your stats are right it might just be easier to find a formula for them.

Im trying to find the formula How would i go about doing this?

It seems to repeat the 2, 4, 6, 8, ... pattern every time it hits an exponential of 2....i.e. 2^x or 2,4,8,16,32,64,128,256,etc

Apparently this problem counts as a test grade, we need to show as much of the set up as we can to get to a right formula(s) for the solution.

The slope is 2 on the points that don't revert back to 2, i.e. values of 2^x.

Does anyone know how to show this?