October 6

Latin squares

 Continuing latin square filling: A,B,C and D only, each once in each row and each column...

Three cities, each has 2 roads out.

Graphs. 

Can we have a road map with 4 cities, each with 2 roads out (roads just connect the cities, or intersect in a regular way, no T-crossings!). 

Can we have 5 cities, each with 2 roads (easy)? 4 cities with 3 roads each? 

What about 4 cities of which 3 cities with have 3 roads each, and one city has just two roads? Is this possible at all?

Robots on the map: How many ways to go?

To recall, we program robots to go from one shape to another. Our starting point is the red triangle, and the robots go one block if you told them the direction. We use only North and West as the direction (otherwise robots will waste their precious charge).

Some place can be reached in more than one way: say from red triangle to yellow pentagon one can go in three different ways:

North West West

West North West

West West North

Try to find for each of the crossings the number of ways to go there (might be tricky for far away crossings!) - and write the numbers on the map. We'll discuss what results later.

Eulerian graphs.

The task is to trace these graphs without retracing and taking your pencil off the paper. The graphs for which this is possible are called  Eulerian. One of these graphs is not Eulerian - which one?

Experiments

Understanding skin conductivity using advanced microelectronics from Radio Shack!