## Posts tagged ‘M&M’s’

### Red + Green = Christmas, and 62 Other M&M Color Combinations

‘Tis the holiday season, so every grocery store, pharmacy, and convenience store is now stocking the M&M^{®} Christmas Blend, a joyful combination of red and green button-shaped chocolate candies. It’s unclear whether this mixture actually helps to imbue the holiday spirit, but the consumption of these tasty morsels will make you look just a little more like St. Nick.

As far as I’m concerned, the Christmas Blend — not to be confused with Holiday Mint, which uses a (disgusting) mint chocolate filling — is one of just a few acceptable color combinations. Why? Because it uses colors that can only be found in the original Plain M&M packs, which contain red, orange, yellow, green, blue, and brown.

The original packs didn’t contain white M&M’s — sorry, Freedom Blend (Fourth of July). The original packs didn’t contain pastel colors — hop on by, Easter Blend. And nowhere on God’s green Earth will it ever be acceptable to use white chocolate inside those delectable candy shells — hit the road, Carrot Cake M&M’s. (Yuck.)

As you can tell, I’m a purist, and I have fairly strong opinions about this.

To my knowledge, there are only two other blends produced by Mars, Inc., that satisfy my acceptability criteria:

- Harvest Blend: red, yellow, brown
- Birthday Cake: red, yellow, blue

So, where am I going with all this? Glad you asked.

The Christmas, Harvest, and Birthday Cake blends represent just three of the 63 possible color combinations that can be made from the original six colors. That leaves 60 combinations that are just begging for names.

(A little history. As you may know, I have a quirk. I eat M&M’s in pairs of the same color, so I can place one on each side of my mouth and feel “balanced.” But it’s atypical for a pack to contain an even number of every color. When I near the end, I’m often left with one to six unmatched M&M’s. And I’ve always thought that these various color combinations deserved a name.)

What would you call a combination of red, yellow, and green? Obviously, STOPLIGHT.

What might you call a combination of red, yellow, and blue? Based on the Man of Steel’s outfit, I like SUPERMAN. But Mars, Inc., has already applied the moniker BIRTHDAY CAKE.

What would you call a collection of just green M&M’s? I don’t know — QADDAFI, maybe? (Sorry, dated reference.)

What would you call a combination of orange, green, and brown? I have no idea.

And that’s where you come in.

Below is a Google poll where you can enter a color combination and suggest a name. In early January, for any color combinations that have more than one suggestion, we’ll vote on it. That’s right — crowdsourcing, baby!

But before you scroll and start clicking, let me lay out some ground rules:

- Keep it clean, please, no worse than PG-13.
- No sports teams! Why? Because the Pittsburgh Steelers, Pirates, and Penguins are black and gold… and although yellow is close to gold, there are no black M&M’s in the Plain M&M’s pack, so that combination is not possible. If M&M’s can’t be used to represent my team, then they can’t be used to represent any team. Sorry — my game, my rules. Not to mention, nearly every color combination corresponds to at least one sports team, so it also demonstrates a lack of creativity. Unless, of course, you pick the colors of a team from the Swedish Bandyliiga, but let’s be honest — were you really going to do that?

Some time ago, I tried to craft names for all the combinations on my own, but I failed miserably. You can see how far I got on **this Google sheet**. So you can tell that I really, really need your help.

Have at it, y’all!

If you can’t see the form below, click this link:

**https://goo.gl/forms/jiCEClAMSDTJtHGZ2**

Don’t want to goof around with a Google form? Fine. Place your thoughts in the comments.

### Games My Brain Plays

The French Quarter Festival and the NCTM Annual Meeting took place concurrently in New Orleans last week. So following five days of spectacular conversations and presentations at the conference, I headed to the festival for stage after stage of live music.

I sat on the lawn in Woldenberg Park, and the woman next to me was movin’ and groovin’ to the sounds of The Dixie Cups. I introduced myself, and she replied, “Hi, I’m Rhonda.” And the first thought that went through my head was…

Hard-onis an anagram ofRhonda.

What the hell’s the matter with me?

If you’re looking for a silver lining here — and believe me, I am — it’s that there are no other one-word anagrams of Rhonda. So at least I didn’t ignore a more socially appropriate anagram and jump straight into the blue.

But you have to wonder why that happened at all, instead of just accepting her name at face value and politely, automatically responding, “Nice to meet you.”

My mind has played games for as long as I can remember, often without my consent. The following are a list of some of them:

- Playing License Plate Algebra with the letters and digits on a license plate. For instance, if a Pennsylvania license plate has
*TFT*to the left of the keystone and 567 to the right, and the keystone is then replaced by an equal sign, and some simplifying is done, this reduces to*T*^{2}*F*= 567, and I search for order pairs (*T*,*F*) that make that equation true. - Riding in a car, I’ll pick a speck of dirt on the window and pretend that it’s a laser/bomb/WMD. As I ride along, anything that the speck appears to touch while I look out the window is destroyed instantly.
- Sometimes, I’ll try to figure out what I’d do if a normal, daily event turned into a life-threatening situation (like this).
- Eating M&M’s two-by-two, one for each side of my mouth. (See my ruminations about a quest to find The Perfect Pack.)
- Having to step on an equal number of cracks with each foot, when walking on the sidewalk through our neighborhood.
- While playing basketball and other sports, getting fixated on a word — say,
*precise*— and when I’m not dribbling or shooting, I’m finding anagrams of the word in my head, or I’ll start to combine pieces of letters — for instance, a*c*and an*i*without its dot could be used to form an*a*— so now I try to make anagrams of*p*,*r*,*e*,*a*,*s*, and*e*. And sure enough, I’ll stumble onto*serape*. But that’s not good enough. I’ll then return to*precise*, combine the*r*and*i*to make an*n*, and now I’ll look for anagrams of*p*,*n*,*e*,*c*,*s*, and*e*. There are none, so I’ll spend the rest of the game in a futile mental search. And two seconds after I convince myself that there are none to be found, the buzzer sounds, and I realize our basketball team has suffered its seventh straight double-digit loss. The defeat wasn’t entirely my fault, but my distractedness surely didn’t help matters, either.

What stupid games does your mind play?

### The Perfect Pack – Redux

Well, glory be!

Two days after lamenting that I had never encountered a perfect pack of M&M’s, and just one day after showing that, on average, only 1 in 64 packs will contain an even number of each color, it finally happened. I bought a pack of M&M’s at the 7-11 (which reminds me of another great problem), and it contained 54 M&M’s in the following distribution of colors:

- Blue – 18
- Brown – 6
- Green – 8
- Yellow – 6
- Orange – 12
- Red – 4

According to the M&M website, the proportion of colors is supposed to be blue, 24%; brown, 13%; green, 16%; yellow, 14%; orange, 20%; and red, 13%. The distribution of colors in the pack that I purchased differs from the expected amounts slightly. But, who cares?

The important point is that there were an even number of each color in the pack! ‘Tis a glorious day!

### The Perfect Pack – My Solution

Here’s a question I posted a few days ago:

A standard pack of M&M’s contains pieces of six different colors. What is the probability that there will be an even number of M&M’s of each of the six colors?

As far as I’m concerned, the type of pack you select is irrelevant, as is the proportion of the colors within the pack. Even though MARS^{®} claims a certain proportion for the mixtures at the factory, the proportion of colors varies from bag to bag. Therefore, my solution is independent of the number of M&M’s.

For each color, the number of M&M’s will be either even or odd. Consequently, the probability of having an even number of one specific color is 1/2. Since there are six different colors, then the combined probability of having an even number of every color is (1/2)^{6} = **1/64**.

I’ve eaten way more than 64 packs of M&M’s in my life, so I’m surprised that I’ve never encountered a “perfect pack.”

### The Perfect Pack

I have a quirk.

Okay, truth be known, I have many. But this post is only going to elaborate on a particular mathematical quirk that I have, which involves eating M&M’s. (Most of my other quirks aren’t interesting enough to warrant a blog post. And those that are probably shouldn’t be publicized.)

I have to eat M&M’s in pairs of the same color. I place two in my mouth at a time, and I chew one on each side. I can’t eat them one at a time, and I can’t eat two M&M’s of different colors at the same time. It’s a balance thing. I’ve done this since I was a kid, and whether it’s just a bad habit or a deeply engrained compulsion, I don’t worry about it too much. Sure, it’s a little weird, but on the OCD continuum, it’s not a big deal. I mean, it’s not like I use a ruler to ensure that stamps are placed exactly the same distance from both sides of the envelope. (Though I have considered it.)

So, the math of this. I have been searching for the “perfect pack of M&M’s,” one in which there is an even number of every color. That way, I won’t have one leftover after I eat the others in pairs. I don’t know how many packs of M&M’s I’ve eaten in my life, but I’ve yet to find a perfect pack. Consequently, it would seem that the experimental probability of such an occurrence is 0. But what is the theoretical probability?

Stated formally, here’s the problem:

A standard pack of M&M’s contains pieces of six different colors. What is the probability that there will be an even number of M&M’s of each of the six colors?

I’ll post my solution in a couple days. In the meantime, here are two math jokes about M&M’s:

How many mathematicians does is take to make a batch of chocolate chip cookies?

Two. One to mix the batter, and one to peel the M&M’s.

How do you keep a math graduate student occupied for hours?

Ask him to alphabetize a bag of M&M’s.