Math = Love: Vacation Math - Sundae Possibilities

## Friday, July 18, 2014

### Vacation Math - Sundae Possibilities

Prepare to gasp, guys.  I've got something to share today that ISN'T a poster.  Shocking, right?

A couple of weeks ago, I went on vacation with my parents and sister.  My sister and I had never been to Colorado, and my parents hadn't been since they were kids.  So, Colorado it was.  We ended up making a giant circle.  Oklahoma to Kansas to Colorado to New Mexico to Texas and back to Oklahoma.

On the last day of our trip, we stopped at Denny's for dinner.  While waiting for our food to be prepared, I decided to glance at the extra menus that were at our booth.  That's when I discovered something exciting.  A math problem!

There are more than 80 ways to build your own Sundae.

Of course, I had to check out their claim.  So, what are the choices for building your own Sundae?

Pick Two Scoops of Premium Ice Cream.  There are three difference ice creams to choose from.  I count six different ways of choosing my ice cream.  VV, VC, VS, CS, CC, SS.

Pick A Topping.  There are three different toppings to choose from.

Pick A Crunch.  There are three different crunches to pick from.

So, by my math, there are 6 * 3 * 3 ways to build a sundae.  This multiplication yields on 54 ways to build a sundae.

Am I missing something?  Did I make a mistake somewhere?  Or do they really not know how many sundae possibilities there are?

The picture on the menu page showed whipped cream on top of the sundae.  This isn't listed on the options.  Adding the possibility of whipped cream or no whipped cream would change my number of possible sundaes to 54*2 or 108.  That is more than 80, but I'm not satisfied by that.

1. Here's what I think... You don't have to add a topping or crunch, so wouldn't that make 4 choices for each? So, 6*4*4=96.

1. This is the way I thought about it, too.

2. I didn't think about the fact that you don't have to add a topping or crunch. Very interesting idea!

2. Maybe when they day "build" they mean CV is different from VC, so there are 3 ways for the first flavor, three ways for the second flavor, three ways for the sauce, and three ways for the topping. This would yield 81 and maybe they rounded to 80?

1. This is the way i solved this problem with a tree! i got 81!

3. My theory: they picked a number and hoped a math teacher would never walk through their door ;)

I've always had a secret desire to march into a Subway and demand they let me count everything they have, just so I can work out how many sandwich combinations are possible. I get very distracted while waiting to order there.

4. Yep, they used the counting principle: 3*3*3*3=81, not taking into account that options like VC and CV are the same thing. At least they tried, I guess.

I like Shaun's theory!

5. Well...they do say there are MORE than 80 ways. Are they wrong?

6. This has been bothering me since I saw the menu at Denny's and looked it up to find this post. I believe they did not take into account that VC and CV are the same thing. If you consider VC and CV to be different then there are 81 ways. I think that is splitting hairs. Can imaging a Denny's spokesperson foaming at the mouth and saying, "IT'S DIFFERENT!!!". No it is not. There are 54 ways.

1. Oh no. Meant to say VC and CV are NOT the same thing.

2. Well I don't know how Denny's builds their sundae's but if they build them vertically then CV and VC are different things because a different flavor is on top each time.

7. If they did consider CV and VC to be the same, but took into account that you could decide to not have a topping or a crunch, this would give 6*4*4 options, 96 total.

I'm sure there's some marketing guru who can explain the psychology of choosing 80 to be the number printed instead of one of the other numbers that have been found.

8. You can repeat the scoop flavor...aka vanilla + vanilla. Thus making the problem, 3*3*3*3 = 81