Math Circle Activity Database
Place our numbers into the cauldrons in ascending order – you can choose which cauldron each one goes in. However, if two numbers in one cauldron add up to a third number in that same cauldron, they bubble up and cause an explosion! This means that all the numbers, leave the cauldrons, and you must start all over again.
Our goal is to find the largest number we can place in our cauldrons without them exploding… do you think you’re up for this daunting task?
The Pancake Problem, first posed in 1975, is a sorting problem with connections to computer science and DNA rearrangements, which leads to discussions of algorithms, sequences, and the usefulness of approximations and bounds.
The original problem was first posed by mathematician Jacob Goodman under the pen name “Harry Dweighter” (read it quickly) in 1975, and it has delighted math enthusiasts (including undergraduate Bill Gates) ever since!
Merriam Webster defines gerrymandering as “the practice of dividing or arranging a territorial unit into election districts in a way that gives one political party an unfair advantage in elections.” This activity tries to make sense of that definition using a few examples.
A town faces an epidemic of zombies! Luckily, the virus has just started to spread and the infected are able to stave off their hunger for human brains… for now. In fact, they’re willing to work alongside the remaining humans to help them get across a river to safety. Can you get all the humans and zombies across safely?
Your regular commute begins at your house and ends at your office at the corner of 5th street and 6th avenue. You have been making this trip for years, but you are the restless (or adventurous) type, and you try to take a different route each day. At some point, you start to wonder how long it will take you to try all of the routes.
Oh, did I mention that you have to avoid the zombies?
For the Math Mind Reading Trick, you’ll need a volunteer who’s willing to have their mind read. The person performing the trick holds out the four cards and askes their volunteer to pick a number (whole numbers only, no fractions allowed!) between 1 and 15 and keep it a secret. Next, the mind-reader asks the volunteer if their number is on the cards one-by-one. The volunteer answers the questions with yes or no answers, and with some magic and a little math, the mind-reader figures out their number!
Start with an nxn grid – you pick the size. Now, split the grid up into (at least two) any-sized squares and rectangles, as long as you don’t repeat the same sized square or the same sized rectangle twice. That’s it! Pretty simple, right? But you might be wondering: “What’s the point?” That’s where it gets a little more tricky. The goal is to find the lowest possible score of whatever n-sized grid you choose. To “score” your Mondrian art, take the area of the largest rectangle or square and subtract from that the area of the smallest.
Students will explore a game between two players moving a chess Queen from place to place on a square grid. The Queen may move any number of spaces to the left, any number of spaces downward, and any number of spaces on the downward-left pointing diagonal. Each player takes turns using these moves. Whoever gets the Queen to the bottom-left square first wins!
Skyscrapers come in so many different sizes! Sometimes you can’t see small skyscrapers if tall ones are in front of them. Using clues about how many skyscrapers you can see from each side you look at them, can you figure out the layout of the entire city?
Each puzzle is a rectangle made up completely of smaller squares. These squares have numbers inside that represents the length of their sides. Just knowing a few of the squares side lengths, can you figure out all the size of all the squares in the puzzle?
The rules are simple: you want to place the sheep on the board so that the wolves can’t eat them. A wolf can eat a sheep if it has a direct path to it – or is in same row, column, or diagonal as that sheep. Can you place all your wolves and sheep on an nxn grid so all the sheep are safe?