Hi all,
got this problem in some silly newsletter- and for the life of me, can't get
the answer they give!
the problem is as follows:
Miss Tryon is the teacher of a large class of girls at one of our more
enterprising schools. She is responsible for several subjects, including
what is vaguely called "handwork," but her principal interest is in
mathematics.
"I tried an interesting experiment this week," she told me. "I had available
a large number of beads. They were of three colors: red, yellow, and green.
"I showed my girls how to make seven-bead bracelets-the beads are just
strung on threads at regular intervals-and then I suggested that each girl
should make a bracelet for herself. My only condition was that she should
use three beads of any one color; two of a second color; two of a third."
"And what was the experiment exactly?" I asked.
"Why," said Miss Tryon, "I wanted to see how many different bracelets were
produced by these haphazard instructions. There were thirty-two, which is
about what might have been expected. It would have been possible-but only
just possible-for every girl to construct a bracelet different in appearance
from all the others."
How many girls are there in the class?
-end of problem---
Now, the answer to this, according to the newsletter is 54.
My count is like this:
1. there are 3 colors to choose the three beads from.
2. For each of the above, on the bracelet there can be either three beads
together, or two together one in-between the rest (3 ways to do this), so
total 4 ways for the 3 beads
3. For each of the above, there's 6 ways to place the remaining 4 beads -[4
choose 2].
so, I am getting 6*4*3=72.
am I counting wrong or what?
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
