Happy holidays from Expii! Hope you are have a happy and wonderful time with loved ones. Aside from opening presents and drinking hot cocoa, celebrate the season with Solve set 55: Holidays! From wrapping presents to binary christmas trees to yummy fruitcake, test your math skills. This set includes trial and error, solstices and equinoxes, surface area, exponential growth and more.

Question 1: This Presents a Problem

You have a large cubical box which contains 1000 cubical chocolates, arranged in a 10x10x10 grid pattern, each in an individual box. You have to decide if you want to wrap the large box or wrap each of the individual boxes. What is the ratio of the amount of wrapping paper needed for individually wrapping the 1000 smaller boxes, over the amount of wrapping paper needed to wrap the single large box?

 

Have you been to the Christmas Tree at Rockefeller Center? Try out Question 3: O Binary Tree:

The Christmas Tree at Rockefeller Center in New York City is an annual tradition. The 2016 tree is 94 feet high and 56 feet wide. Conveniently, tree weight does not scale with the volume of the cone determined by the tree, because the internal branching pattern makes the tree sparser inside than at the fringes. Evergreen trees grow this way so they have a large surface area to capture sunlight while the interior can support the tree structurally. To see how quickly a branching structure can expand, consider a growth process which starts with a single branch, forking into two sub-branches after a foot of growth, and where every sub-branch forks into two more sub-branches after a foot of growth. After how many feet of growth would there be 1 million sub-branches?

Keep solving and have fun. Have a happy new year!

 

Solve set 55: Holidays