A professor of Information Theory at the University of Bristol did some interesting research on the statistics associated with Christmas. Professor Johnson spent most of the pandemic helping explain the various Covid statistics to the population. As things have slowed down, he decided to explore the statistics associated with Christmas.
He looked at the statistics on decorating your tree, stacking tree decorations, wrapping presents, to selecting favorite chocolates, and of course Santa. He explored the math of everything from what happens if a person miscalculates the amount of time needed to defrost or cook a turkey to figuring out how to seat everyone at the table for Christmas dinner.
In regard to decorating the tree, most people try to create a random pattern of decorations so there are no two of the same color right next to each other. Humans are not really good at randomness so we cannot create truly random patterns. So, let's say you have 100 ornaments to hang on 100 branches, then if you "randomly" place the ornaments on the branches, you'll end up with all the decorations placed on about a two thirds of the branches. This means about 37 branches will be bare and other branches might have up to four ornaments on them.
Using Maclaurins inequality, they've found that the best shaped box to use to save money and wrapping paper is a cube because cubes have the smallest volume. In addition, the most popular flavor of chocolate at Christmas time is chocolate orange. If you want to save money on wrapping it, don't buy it in the box with the individually wrapped orange, buy a regular shaped chocolate bar in that flavor.
According to this same mathematician, the 12 days of Christmas song represents the numbers in Pascals triangle. On the first day, you get one partridge in a pear tree. On the second day, you get two turtle doves and the partridge in a pear tree. This means you got 1 on the first day, 3 on the second day because 1 + 2 =3. On the third day, it would be a total of 6 since 1 + 2 + 3 = 6. If you do this for every day, you see Pascals triangle with 1, 3, 6, 10, etc. At the end of the 12 days, you will have received 364 presents in total.
It is well known that those glass ornaments break so easily. About 400 years ago, someone decided that the best way to store them was in a hexagonal shapes in layers so each bauble touches 6 others in one layer. The next layer is set so the baubles are over the openings of the lower layer. It wasn't until 1998 that someone was able to prove this is correct.
Finally, let's look at those boxes of chocolate where there are a few flavors that are not that popular. If you say the box has 30 total pieces, where 24 have the preferred flavors and 6 do not, then you can calculate the possibility of getting a less desirable flavor is 6/30 = 1/5 = 20 percent. This is assuming people eat the flavor they chose but what if they return the nasty flavor and exchange it for a preferred flavor. That changes the statistics and raises the numbers so you are more likely to get a nasty one toward the end of the chocolates left in the box. Let me know what you think, I'd love to hear. Have a great day.
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