For years we've been doing an M&M packet statistical research project
(in an elementary school I work with).  Each student gets a packet of
M&Ms to count, record colors, numbers, percents, etc.  M&Ms work well
because there are about 6 colors and, most importantly, because the
colors are NOT EQUALLY DISTRIBUTED.  In the typical package (it can
vary, of course) there are many more browns, and some colors (e.g.
orange and blue, used to be tan) are much rarer.   Various people over
the years (e.g. Cecil Adams) have provided specific percentage counts
for the different colors.

ANYWAY.  My question is this:  this year, we have a student in class
who is so allergic to peanuts that we can't use M&Ms because they
might contain trace amounts of peanuts.  We are searching for another
candy we can use instead.  BUT we aren't coming up with any ideas,
because we need something that has a moderate number of colors (say 5-7)
with CLEARLY DIFFERENT PERCENTAGE DISTRIBUTIONS.  Therefore, SKITTLES
DON'T WORK.

We obviously can't use Reese's Pieces, even if they did work, since
the whole point is to stay away from peanuts.

Any other ideas?  I want a specific candy product in mass production
(or otherwise easily available).  I'd like the source for your
information about the color distribution.  And, sadly, I don't believe
there is an answer, so I'm not holding my breath.  Please don't just
guess -- I've already done plenty of that.

---

Request for Question Clarification by alienintelligence-ga on 05 Aug 2002 18:14 PDT

hi dbalbert

Maybe some type of gumball, or hard candy?

We have to insure it's not made in a
plant that makes peanut products too,
right?

Pixie Stix? 

scouring the sweet side of the net...
-AI

Why not use one of my favorites candies as a child, SMARTIES!  They
come wrapped in plastic rolls and they are inexpensive.  Following is
a list of ingredients according to the Ce De Candy Inc. company, maker
of smarties:

Smarties Ingredients (Includes X-Treme Sour & Tropical): Dextrose,
Citric Acid, Calcium Stearate, Artificial Flavors and Colors (Red 40
Lake, Yellow 5 Lake, Yellow 6 Lake, Blue 2 Lake).

You should have no problem with possible peanut contamination.  You
should check with the manufacturer first to be sure.

Smarties can be purchased in drug chains, supermarkets, convenience
stores, wholesale clubs and your corner store.  Ce De Candy Inc. Web
site can be found at: http://www.smarties.com.

There is also a site devoted to the color distribution of Smarties
candies.  The site provides statistical problems with possible
solutions.  The level would be too high for elementary students, but
it's worth checking out.  It shows that Smarties are a good choice
when looking at random color distribution!

The site can be found at http://www.mathrec.org/intro/

SITES MENTIONED

Ce De Candy Inc.
http://www.smarties.com.

Welcome to Mathematical Recreations -- Distribution of Smarties
http://www.mathrec.org/intro/

GOOGLE SEARCH TERMS USED
'color distribution smarties'

Best of luck!

d_p_lee-ga

---

Request for Answer Clarification by dbalbert-ga on 05 Aug 2002 19:14 PDT

I've considered smarties, but I haven't noticed any definite NON-EQUAL
distribution pattern, nor did the website you pointed me to have any
specific information on that score.  I was hoping for some more
specific information here before I started buying huge quantities and
counting them.

At least with Smarties I like them enough to consider that if I
haven't any other options -- I'm afraid I can't say the same for
Jujubes.

Any more information on color distribution of smarties?  And how many
colors do they really come in, in a typical roll or two?  I don't have
any in front of my but my gut reaction is that they're pretty much all
white, yellow, or pink.  Are there really 5-7 colors?  I'll go take a
look in a store tomorrow.

I don't need information on statistical puzzles for these candies -- I
have the whole unit written up.  I just need a substitute for M&Ms. 
If you have more information about Smarties I'll certainly consider
them; otherwise that seems like another dead end.

---

Clarification of Answer by d_p_lee-ga on 05 Aug 2002 20:57 PDT

Smarties come in 7 pastel colors: orange, green, white, pink, blue,
yellow, and purple. (The colors are easily counted on the graphics on
the http://www.smarties.com Web site)

The only mention of color distribution for candy (other than M&Ms) on
the web was the site I referred to originally.

I cannot back this suggestion up with any data, but you may consider
NECCO Wafers [http://www.necco.com/].   NECCO Wafer rolls contain 8
flavors and colors: lemon (yellow); orange (orange); lime (green);
clove (purple); cinnamon (white); wintergreen (pink); licorice
(black); and chocolate (brown). From my experience with them, there
are definitely less black and purple ones [licorice and clove (*ugh*)]
than any other color in any roll.  I will send the company and email
to confirm whether they are evenly distributed.

SITES MENTIONED

Welcome to NECCO - http://www.necco.com

---

Clarification of Answer by d_p_lee-ga on 06 Aug 2002 09:50 PDT

According to the folks at NECCO:

"NECCO Wafer flavors are made in 550 pound batches each day. They are
then dried and after that mixed together. It is not a scientific
process and what appears in a roll or bag is totally random. They all
start out in equal batch quantities, however."

I will check with the Smarties folks.

Best,

d_p_lee-ga

Well, I still don't have a definitive answer.  I suppose this was a
reasonable amount of information for a low-dollar question, but so far
all we've done is rule out Necco, since the colors are all equally
likely.  Please do let me know if you hear from Smarties.  If the
colors are NOT all equally likely, then that may be our best bet, but
if they are then I'm still stuck....

Jujubes seem to come in a random distribution of colors, as do most
inexpensive jelly beans (Brach's, Smuckers, and such.) The "gourmet"
jelly beans like Jelly Belly would have too many different colors, but
cheap jelly beans might be just the thing for your project. Not much
chance of peanut residue on 'em.

Another possibility is plain old Lifesavers in the original 5-flavor
roll. I have been mighty disappointed sometimes when there weren't
enough cherry-flavored ones. They seem very random indeed!

Hi!

As it happens, I have a horrible sweet tooth and keep a large basket
of candy on my desk - which includes Smarties!

Smarties come in white, yellow, pink, orange, green and purple.  And
looking at the Smarties FAQ, you can see what flavors they are:

Smarties FAQ
http://www.smarties.com/answ.htm

Pulling open a 15 smartie roll, I find:  6 white, 3 yellow, 2 green, 4
purple.  No pink or orange.  A second roll shows all colors, a third
shows all but green.  (I'm not going to open those, it's too late for
so much sugar.)  Looks pretty random to me!


--Missy



--Missy

Another good choice would be Sweetarts. They come in six flavors:

Cherry (pink), grape (purple), orange (orange), lemon (yellow), lime
(green), and tropical punch (blue).

I love these things. Once I bought a case of 48 rolls at Sam's
Wholesale Club, and I ate them all in a week. I am certain the colors
in a roll of Sweetarts are randomly distributed. Sometimes a roll
contains a plenitude of the blue ones (yummy) and sometimes the green
ones predominate (yucky)!

I am not sure where you are, geographically, but Smarties are
something entirely different in the rest of the world. They are more
M&M-like. I know you can get them in Canada, they are made by Nestle.

Just my two cents.

I know about the chocolate variety of Smarties.  They're not widely
available here (that is, one can get them at specialty import stores,
but they're on the expensive side).

I think I'll have to check out a few rolls of smarties and (ugh) Necco
wafers (are those things made of chalk?).

Thanks for all the answers and comments.