## Christmas Problems
If you're in the mood for a computation-themed Christmas, here are a few problems to tinker with for when it's chilly outside and there's not a lot to do. Each of these problems is based on a chapter that we've read in a meeting.
If you'd like to add your own problems, please fork this repository and submit a pull request. You're more than welcome to do the same if you have a cracker of a solution that you'd like to share.
Generate random numbers that approximate the shape of a cut-out Christmas tree:
These random numbers should come in pairs (two-dimensional vectors). Each pair corresponds to an (x, y) coordinate of the image plane. All generated points should lie within the bounds of the tree and should appear in that region with an equal probability.
Upgrades:
- Add a "trunk" at the base of your tree and a "star" at the top of your tree
- Decorate your tree with some colour
- Real trees are three-dimensional, so yours should be too!
The Koch Snowflake is a famous fractal that has an infinite perimiter, as well as many other interesting properties. Generate a Koch Snowflake:
Provide a mechanism to set the number of iterations that should be computed when generating the snowflake.
Upgrades:
- Colour your snowflake such that each triangle's colour intensity is inversely proportional to its size
- Allow users to "zoom" in on regions of your snowflake
- Real snowflakes are three-dimensional, so yours should be too!
Construct a proof that shows that fewer partridges are gifted than "Lords a Leaping" in the famous carol "Twelve Days of Christmas."
Upgrades:
- Write something that can mechanically prove the theorem
- Convert derived axioms back into meaningful English
Real proofs are three-dimensional, so yours should be too!