# Thread: Pre-Algebra 'People in a Circle' Problem

1. ## Pre-Algebra 'People in a Circle' Problem

Hi -
I'm having trouble figuring out this algebra word problem: part b & c actually are what is difficult for me -

"Suppose 19 people are arranged around a circle and numbered from 1 through 19. Starting with 1, eliminate every second person. Thus for every 19 people the elimination is 2, 4, 6, 8, 10, 12, 14, 16, 18, 1, 5, 9, 13, 17, 3, 11, 19, 15. The remaining number is 7.

a. For values of n from 2 through 20, make a table showing the remaining number after the process of elimination. (done that!)

b. Formulate a conjecture about which values of n have 1 for the remaining number. (help!)

c. On the basis of the conjecture in b and the pattern that appears, find the remaining number if n = 300." (help!)

2. Hi,

What you need to do is to look at the table that you created in part 1 and look for all the occasions where the remaining number is 1, noting the value of n that you started with.

You should see some kind of relationship with all of the n's that you find. For example, are they all even, all odd, all squared numbers?

Using this rule that matches all of the n's you should be able to determine the remaining number for 300 in the final part of the question.

3. my son has this same problem, and I am totally confused with the answer. I'm assuming it has to do with the power of 2, and there is something important with the last number being 1. but I'm still lost.