## Posts tagged ‘form’

### 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.

### Stolen Truck Solution

Last week, I posted a modified version of Marilyn Burn’s horse problem, and I asked you to submit your answers. I received 331 responses; thanks for participating! An analysis of the submitted responses appears below, but first, a few comments and several different solutions.

My friend Jeane Joyner of Meredith College uses this problem in teacher and parent workshops. She said:

I have folks move to corners of the room — makes money, loses money, and breaks even. Then each groups selects an ambassador to go to the other groups to see if they can persuade folks to move. Fun!

Without further adieu, here is the answer: **The man made $200.**

**Solution #1:** He spent 600 + 800 = $1,400, and he received 700 + 900 = $1,600. That’s a profit of $200.

**Solution #2:** Assume the man started with $1,000 in his bank account. He bought the truck for $600, so he had $400 left. He then sold it for $700, so his account increased to $1,100. He bought it back for $800, so he had $300 left. When he sold it for $900, his account increased to $1,200. Since he started with $1,000 and ended with $1,200, he made a profit of $200.

**Solution #3:** Use a number line to show how his amount of money changed.

After the four transactions, he is at +200 on the number line, so he made a profit of $200.

**Solution #4:** Some people find it confusing that he buys and sells the truck twice. It might be easier to think of him doing these transactions with two different vehicles. For instance, what if he bought a truck for $600 then sold it for $700, and then bought a car for $800 and sold it for $900? It might be easier to wrap your head around that.

Approached that way, his actions represent two separate events. The first time he bought and sold the truck, he paid $600 and sold it for $700. That’s a profit of $100. The second time, he bought it for $800 and sold it for $900. That’s another $100 profit. In total, he made $200.

After I posted the problem, a friend on Facebook asked, “Huh? How is that supposed to be hard?” Edward Early of St. Edwards College responded:

Sadly, I’ll only be surprised if there is a strong consensus for the correct answer. I’ve been teaching math too long to expect that to happen.

Of the 331 respondents, only 325 submitted usable responses. (Chalk this up to bad phrasing on my part. I asked folks to “enter a negative number if he lost money, 0 if he broke even, or a positive number if he made money.” I was meaning for people to enter the amount he lost or made, but some respondents entered a positive number that wasn’t possible in the context of the problem, such as 1 or 12. I think they thought they should enter *any* positive number to indicate that he made a profit. And one wiseacre responded, “a positive number.” Sorry, not even partial credit for that response!)

Of the 325 usable responses, 228 (70.1%) were correct. Answers from the other 28.9% ranged from ‑600 to 900, with 0 (28 responses) and 100 (47 responses) chosen most often. The chart below shows the distribution of incorrect responses. (Data for 200 has been removed since it overwhelms the others; its bar would be more than four times the height of the next highest bar.)

The vast majority of respondents (276) were 16 years of age or older. The 49 responses from people age 15 or younger looked like this:

Age | Responses | Correct Responses |

6 | 1 | 0 |

7 | 1 | 1 |

8 | 2 | 1 |

9 | 4 | 1 |

10 | 4 | 1 |

11 | 1 | 1 |

12 | 4 | 3 |

13 | 15 | 11 |

14 | 8 | 7 |

15 | 9 | 7 |

Interestingly, the under‑16 crowd, with 67.3% correct responses, did almost as well as the over‑16 crowd, which had 70.6% correct responses. And for the 11- to 15‑year old subset, an astounding 78.4% of the responses were correct.

From this, we can conclude that these youngsters are smarter than the rest of the population… but of course we already knew that, because teens and pre-teens know *everything*, right?

### My Favorite Game, Social Media Style

Inspired by Planet Money’s Pick A Number contest, and buoyed by a story about how NCTM President Mike Shaughnessy recently used my favorite game with a group of students at Albuquerque Academy, I’ve decided to conduct an online experiment using a Google Docs form.

If you’ve got a minute and are willing to participate, read on.

The rules for my favorite game are as follows:

- On a piece of paper, everyone playing writes down a positive integer.
- Show your number to a neighbor (for verification purposes only).
- The winner is the person who wrote down
*the smallest integer not written by anyone else*.

In order for this psychological math strategy game to be any fun, you need one important piece of information — how many people are playing. If played as a solitaire game, you *should* win every time. But if played with a group of 50, well, some real thought will need to go into your choice. Consequently, I’m going to limit the game to 100 players. (Well, sort of. What I’m actually gonna do is break the total number of responses into groups of 100, and I’ll consider each set as a separate game. So it’s not exactly the same, but this should allow you to play using the same strategy as if you were playing with just 99 other people.)

For this online version, the second step of the rules — show your number to a neighbor — is unnecessary. So all you need to do to play is enter your number. (I’ve also asked for your name and email address, too, just so I can give you proper credit and contact you if you win. But those are optional. If you do supply your email address, cross my heart, there will be no spam or third‑party solicitations.)

**[Update]** This game was originally run for one week, Nov 28 – Dec 5, 2011. The results of that initial trial (based on 1,042 entries) are available at the link given below. That said, I see no reason to prevent others from participating and, from time to time, I will update the results page to reflect new data.

**https://mathjokes4mathyfolks.wordpress.com/2011/12/05/results-for-my-favorite-game/**

If you have difficulty accessing the form below, click this link.