# Cave person games

What kinds of games can be played using just stones? It turns out quite a few! In this session we investigated three games in particular. Continue reading Cave person games

# Taking in the whole room

Suppose you have a room, and you need to guard it using ceiling mounted cameras. Assume the cameras can see in 360 degrees. If the room is very simple, such as a square shape, you can get away with just one. But if the room is more complicated, say with nooks and crannies, you may need many cameras. How can you find how many? Continue reading Taking in the whole room

# Multiplying points in the plane

It is easy to add points in the plane “coordinatewise”, that is, by writing (x,y)+(z,w)=(x+z,y+w). This even has a very nice geometric interpretation: completing the parallelogram with first three corners (0,0), (x,y), and (z,w). But it isn’t easy to multiply points because the simple rule (x,y)*(z,w)=(xz,yw) doesn’t allow division. In this activity we looked for something better. Continue reading Multiplying points in the plane

# Graph isomorphism

A graph is a collection of dots (called vertices) joined by curve segments (called edges). It doesn’t matter how you name the vertices and it doesn’t matter where you put them in your drawing. Two graphs are called isomorphic if you can rearrange the way one of them is drawn to make it look like the other. So for example you might convince yourself that a pentagon and pentagram are isomorphic to each other.

# Tournament Winners

Imagine three friends play a game. Mia beats Alex, Alex beats Siki, and Siki beats Mia. Which one of the three, if any, should we consider to be overall winner? In this session, we consider the idea of a tournament, which is a series of one-on-one win-or-lose games in which every player plays everyone else one time. Continue reading Tournament Winners

# Counting simplified fractions

We all know that many fractions can be simplified, for example, 6/20 may be better written as 3/10. So how many fractions (less than 1) really use a denominator of 20? The answer turns out to be exactly eight… 1/20, 3/20, 7/20, 9/20, 11/20, 13/20, 17/20, and 19/20. But is there a rhyme or reason to this answer? Continue reading Counting simplified fractions