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The classic holiday song “The Twelve Days of Christmas” is a delightful enumeration of increasingly grandiose gifts presented on each of the twelve days of Christmas. Mathematically inclined listeners may notice a pattern and wonder: How do you end up with a total of 364 gifts? To derive this total, we need to delve into how the gifts accumulate over the twelve days. On each day, a set of gifts is given, and each set is cumulative with the gifts given on all previous days. Here’s a breakdown of how the process works.
Understanding the Song’s Pattern
The song presents a list of gifts, with each day building on the previous days' gifts. Here’s a brief reminder of how it goes:
- On the first day of Christmas, my true love gave to me: a Partridge in a Pear Tree.
- On the second day of Christmas, my true love gave to me: two Turtle Doves and a Partridge in a Pear Tree.
- On the third day of Christmas, my true love gave to me: three French
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