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62,950 Points

A Scientific Approach!

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.

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.

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 [

Thank you for reading!

Best regards and happy mathematical thinking,

Kevin C. Cross, Sr. (mwvisa1)

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