19 arranged in circle; starting w/ 1, elim. every 2nd person

[Willgrade7]

I'm having trouble figuring out the algebra word problem to help solve this problem: part b & c actually are 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!)

 

[Denis]

Re: Pre-Algebra Word Problem

Same as ye olde locker doors puzzles; go here:

http://www.google.ca/search?hl=en&q=loc ... arch&meta=

 

[Deleted member 4993]

Re: Pre-Algebra Word Problem

"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!) <<<< Please share with us the table - from which 'b' needs to be answered

 

[Denis]

  1     2     3    4     5     6     7    8     9   10   11   12   13   14   15   
  1     1     3    1     3     5     7    1     3    5    7    9   11   13   15

  16   17    18   19*   20    21    22   23    24   25   26   27   28   29   30   31
   1    3     5    7*    9    11    13   15    17   19   21   23   25   27   29   31

* your 19 = 7

top line: number of persons in circle
bottom line: the survivor

Pretty clear pattern, right?
If that's not enough for you to finish off, then you need more help than you can (usually!) get here :shock: