# Coffee beans and math

My dad had a backache last week, so he went to the doctor. First the scale showed he lost 30 pounds in the past month, which clearly wasn’t right. The scale must be broken! Then they took his blood pressure, which was 60/40, which clearly wasn’t right. The cuff must be broken!

No, it turns out my dad was broken. The doctor called an ambulance and sent him to the hospital – his blood pressure was so low it wasn’t safe for him to drive. He left me a voicemail asking me to drive up the next day to feed his cat. (The man has his priorities!)

Visiting hours didn’t start at the hospital until 11 a.m. the next morning, but I was so anxious I was all ready to go an hour too early. I went to my favorite coffee shop, Take 5, to brood over a cup of tea.

As soon as Bernadette took my order, she put an entry form in front of me. They were having a coffee-bean contest! Guess how many coffee beans were in this jar:

And you win this chocolate gorilla:

Well…that sounded like a MATH PROBLEM to me, and nothing cheers me up like doing some MATH!!

Using a tape measure (which is allowed by the rules!) I measured the circumference and height of the jar, and made the following back-of-the-envelope (back-of-the-entry-form?) calculations:

I calculated that the volume of the jar was 170.7 cubic inches, and the volume of a coffee bean was 0.0293 cubic inches. I figured there were five thousand eight hundred twenty six and a half beans in the jar.

I thought math would get me in the general ball park, but there were so many potential sources of error (coffee beans vary in size, there was also air in the jar between the beans, my measurements may not have been spot-on accurate) that I really wasn’t sure how close I would be.

Imagine my excitement when the final bean was counted and I finished in second place! I was only off by 66 beans – there had been 5,761 beans in the jar. Someone (whose favorite number was seven) guessed 5,777 beans and walked away with the chocolate gorilla. But that’s okay, as a runner-up I was awarded:

…gift certificates for a free cup of tea!

But what I really want to know is…who counted all those beans?!

### 4 Responses to Coffee beans and math

1. Very impressive Alice!! I always underestimate in those contests!

Molly’s school had a family math night for a few Wednesdays and one of the guessing games was guessing how many inches of red licorice rope was in a jar.

2. If it was me, I wouldn’t count the beans. I’d weigh a sample of 25 beans, get an average bean weight, and then weigh all the beans in the jar. You’ll get a number close to the actual number of beans without actually counting them. Unless you have a lot of guesses that are very close together in the right ballpark, this is probably close enough for practical purposes.

3. Though it occurs to me that if you *do* have to actually count them, you should get an accountant…they are ‘bean-counters’, right?

4. Mike Wininger

Nice work, Alice. Your approach is elegant and straight-forward. And clearly: it is accurate! ..I am curious to know whether the winning entry was a ‘lucky guess’ or based on a calculated estimated that considered different variables or parameter values. In any case- enjoy the ‘fruits’ of your labor (yes, I think that the coffee bean is a fruit of the coffee tree), and Feel better, Ron Rentz!