## 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.

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• 1. The Perfect Pack – Redux « Math Jokes 4 Mathy Folks  |  September 5, 2010 at 5:45 pm

[…] 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 […]

• 2. Fergal Daly  |  September 9, 2010 at 3:14 am

I have a similar habit. Colours are not involved but I am really fond of taking even numbers or better still powers of 2 of whatever it is I’m eating.

It also applies in other ways like touching something.

My earliest recollection is being about 5 years old and having to turn around twice because I had already turned twice in the other direction. It’s definitely a balance thing and I think it has waned as I have got older but if most strong with regards to he eating things.

• 3. venneblock  |  September 9, 2010 at 5:49 am

I have a balance issue, too. I used to play with my fingers by touching my thumb to my pinky, then to my ring finger, then to my middle finger, then to my index finger… then I’d go back down, index, middle, ring, pinky. But I’d feel unbalanced because I had just done it on the right hand, so I’d then have to do the same thing on the left hand. But then once I finished, I’d have done the left hand more recently, so I’d have to do the right hand again. But then once I finished, I’d have done the right hand more recently, so I’d have to do the left hand again. Ad infinitum. I’d literally spend hours doing this, until something distracted me, or I fell asleep, or my mom hollered, “Stop playing with your *&\$!^#% fingers!” In high school pyschology, our teacher told us that his brother, who scored a 1590 (out of 1600) on his SAT, did the same thing. Then I didn’t feel so bad, because I assumed it was a sign of high intelligence. In hindsight, I think it’s a mild case of Asperger’s or OCD.

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