Since I first introduced the boys in "The Secret of Terror Castle" several years ago, I have been inundated with requests from their many fans wanting to know the details of how Jupiter Jones calculated the number of beans in the jar that won him the use of a Rolls-Royce and chauffeur for 30 days. Since I am more inclined towards actor direction and the making of films, and not, I am pleased to say, with the mathematical intricacies of calculating the number of beans in a jar, I asked Jupiter to explain how he did it.
Feeling rather pleased that I had to ask, Jupiter removed a pen from his shirt pocket, asked for a piece of paper and drew a jar.
"Mr. Hitchcock," Jupiter began, "there is only one mathematical formulae to calculate the volume of a jar, and that is simply the height by the area of the base of the jar." He wrote the equation on the piece of paper.
Jupiter continued, "There are, however, two stratagem required to solve this conundrum. One is by using "beans" as the measuring unit because the Rent-'n-Ride Auto Rental Company had the jar of beans displayed in their window and wouldn't let anyone touch the jar. The second strategem is to count the beans on one side of the jar so that the diameter and, therefore, the area of the base of the jar can be calculated."
Here Jupiter paused to make sure I was following his line of reasoning and then continued.
"I spent several afternoons in front of Rent-'n-Ride's window counting the number of beans on one side of the jar. I found that the jar was about 23 beans in height and that one row consisted of about 19 beans.
Again Jupiter paused as he wrote the dimensions against the drawing of the jar.
"From this I was able to calculate that the radius of the jar was about 6 beans. I then had all of the information required to calculate that the volume of the jar was equal to 23 beans by Pi by the square of 6 beans. After taking rounding into account, I came up with the correct solution of 2,663 beans."
I must admit that I was surprised at the simplicity of the solution after Jupiter had finished explaining.
"Thank you Jupiter, it is just as I thought." Smiling to myself, I turned my back on Jupiter to face the bookshelves behind me. "Please let me present you with some gifts to reward you for your succinct explanation. Here is a first edition of your first published case, "The Secret of Terror Castle," sent to me by one of your most fervent fans, Seth Smolinske, as well as a signed piece of original Mark Zahn Artwork from one of your soon-to-be-published cases."
And so, fans of the Three Investigators, I hope this answers your questions regarding the "Beans in the Jar" mystery.
NOTE - This was Sam's original entry for the "How Many Beans?" contest sponsored by www.threeinvestigatorsbooks.com, Seth T. Smolinske, and Mark Zahn in August of 2002. Sam wrote: "In keeping with the spirit of a 3I competition I thought a bit of creativity was in order, so I have provided my answer in the form of a short story."