[ugrads] First math competition meeting Tuesday noon
Michael J. Pelsmajer
pelsmajer at iit.edu
Sun Sep 11 14:36:37 CDT 2005
Hi,
It looks like Wednesday at noon is good for most
people usually, but let's start this this week on
Tuesday at noon. Meet in room 119, although we
might have to go somewhere else. Anyone is welcome
to show up. There may be snacks.
Michael Pelsmajer
Here's one you can think about now:
A number of students stand in a circle. Beginning
with student #1 and going clockwise around the
circle (student #2, student #3, student #4, etc.),
the students count off 1,2,3,1,2,3,1,2,3,... The
students who say "2" or "3" leave the circle
immediately. When the count gets back to student #1,
it continues to follow the same pattern (but only
with the students who remain). The last student
remaining wins a prize.
For example, if there are 14 students, the first
round would proceed as follows
student # 1 2 3 4 5 6 7 8 9 10 11 12 13 14
count 1 2 3 1 2 3 1 2 3 1 2 3 1 2
and only students #1, #4, #7, #10, and #13 would be
around for the second round. Since student #14 had
said "2", student #1 will say "3" (and be
eliminated). Round two will proceed as follows
student # 1 4 7 10 13
count 3 1 2 3 1
and hence students #4 and #13 will survive to the
third round. Since student #13 said "1", student #4
must say "2" and be eliminated, leaving student #13
as the winner.
1. Determine the winner if there are 2004 students.
2. Determine the winner if there are n students, for
every positive integer n.
(Modified from
http://math.smsu.edu/~les/POW02_04.html; originally
from Vietnamese Olympiad in Mathematics.)
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