畫圖：像數學家一樣解決難題

We will study about a dozen puzzles (examples: pass a message at a party; coordinate animals crossing a river), and solve them together using diagrammatic representations. The diagrams we'll learn and practice together are from a branch of mathematics called graph theory. They are quite simple -- just some dots connected by lines -- yet powerful for finding solutions to puzzles.

We'll learn some cool properties of graph diagrams, such as when is it possible to trace a pencil from a starting point to an end point while traversing every line exactly once. It turns out that knowledge like that can help us solve puzzles -- for example the traceability property gives the solution of the dominoes puzzle, when we represent the dominoes as a diagram. The key skill we'll practice together is translating a given puzzle into a diagram, and then using the diagram to solve the puzzle. This practice can help with abstract reasoning.

The weekly progression is as follows:
 - Week 1: Introduce and practice working with graph diagrams, via several puzzles including Guarini's Puzzle.
 - Week 2: Learn about Euler paths and circuits in graphs (existence test and algorithm), via puzzles such as Bridges of Konigsberg.
 - Week 3: Practice Euler circuits via the Cave Treasure puzzle. Learn about state-space graphs via Lions and Wildebeest.
 - Week 4: Practice state-space graphs with Water Jug puzzle. Do one final puzzle. Review graph diagrams and how they've helped us solve various puzzles.

No prior knowledge of graph theory is required, only enthusiasm for puzzles!