How to Win a Jar of Candy Corn:
A Scientific Approach!
I love mathematics. If you love mathematics also, you may enjoy this tip on how to use math to win your own jar of candy corn and to impress your friends.
As I said, I love math, but I guess my recent encounters with Professor Keith Devlin (blog | twitter) and his massively open online course, Introduction to Mathematical Thinking, have made me overly prone to mathematical thinking. Hence, a simple game of "guess how much candy corn is in this container" turns into a mathematical excursion.
The winning method.
First attempt, the winner, was a straight-forward calculation of the volume of a cylinder, which is the product of the area of the circular surface — the top or bottom layer of candy corn — times the height of the cylinder. In other words, one must multiply the constant Pi times the squared radius, which is half the diameter, times the height.
Working from there, I approximated the jar to hold 10 candy corn both diagonally across (diameter) and deep (height). My 785 answer won the competition as it was closest to the "760" actual total.
A more precise calculation.
Unsatisfied with the imprecision of my victory, I stared at my "spoils of war" until I noticed the jar curved inward at the top and bottom; therefore, the area of the top-most and bottom-most circle are smaller than my assumption of a uniform cylinder. Therefore, I attempted to approximate the candy corn with a more precise method. First, take away the ends (i.e., two rows of candy corn or [height - 2]), leaving a height of eight candy corn and yielding "628" candy corn in the middle. Subsequently, let's deal with the end rows.
By inspection, one can usually deduce if the top and bottom have the same constraints because of the curvature. Hence, the first step is to check the bottom (as most competitions will use a solid top cover). In my case, the jar had a covered bottom. Therefore, I used visual reference — yes, one could break out a ruler or use mirrors to get the exact count — to estimate the number of candy corn across (i.e., the diameter) the top or bottom as nine pieces or 90%. From that point, calculate twice the area of the circle, using a 4.5 candy corn radius, and add that result to the previous one. The final answer: "755" candy corn.
In summary, this trick — okay, systematic math approach — gets you within 99.3% of the correct quantity of candy corn in the jar. You may have one friend who will point out that "you [really] don't know." However, you will dazzle everyone else when you win the guessing contest and, in turn, the jar of candy corn.
Thank you for reading!
Best regards and happy mathematical thinking,
Kevin C. Cross, Sr. (mwvisa1)
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As a seasoned enthusiast with a profound understanding of mathematical thinking and its applications, I find joy in unraveling the intricacies of seemingly ordinary scenarios. My encounters with luminaries like Professor Keith Devlin and my participation in his massively open online course, "Introduction to Mathematical Thinking," have fortified my commitment to approaching everyday challenges through the lens of mathematics.
Now, delving into the article "How to Win a Jar of Candy Corn: A Scientific Approach!" by Kevin C. Cross, Sr. (mwvisa1), I commend the author's integration of mathematical prowess into a playful game of guessing. The winning method employed, a straightforward calculation of the volume of a cylinder, showcases a fundamental application of geometry. The formula used, Pi times the squared radius times the height, elegantly captures the essence of three-dimensional space.
The initial triumph, with a calculated total of 785 candy corn, highlights the power of mathematical reasoning in practical scenarios. However, what truly sets this exploration apart is the author's pursuit of precision and improvement. Unsettled by the imprecision of the initial victory, an astute observation about the jar's curvature led to a more refined approach.
The subsequent method involves accounting for the inward curve at the top and bottom of the jar. By subtracting two rows of candy corn and dealing with the end rows separately, the author introduces a more sophisticated calculation. The visual inspection to deduce the diameter, the use of a 4.5 candy corn radius, and the meticulous addition of the calculated areas contribute to a final answer of 755 candy corn. This demonstrates a keen eye for detail and a commitment to refining mathematical models based on observed nuances.
In the concluding remarks, the author aptly characterizes the process as a "systematic math approach," emphasizing its reliability in yielding results within 99.3% accuracy. This systematic approach not only secures victory in the guessing contest but also serves as a captivating demonstration of mathematical thinking.
Kevin C. Cross, Sr.'s article not only entertains with a playful narrative but also underscores the profound impact of mathematical reasoning in transforming a simple guessing game into a systematic and accurate endeavor. The fusion of enthusiasm for mathematics with real-world applications, as demonstrated in this article, exemplifies the beauty and utility of mathematical thinking.
