Graph Theory & Networks
📋 What it is
A graph is dots (nodes) joined by lines (edges); it models mazes, maps, and connection puzzles.
🗣️ Coach says
Many escape puzzles are secretly graphs — rooms as dots, doors as lines. The famous “trace this shape without lifting your pen” puzzle is solved by a graph rule about how many lines meet at each dot. See the graph and the rule appears.
🧠 Memory hook
Rooms = dots, doors = lines. Count the lines at each dot to find the path.
😂 Giggle
What did the padlock say when it was finally opened?
"I'm unhinged!"
😲 Whoa!
Graph theory was born in 1736 when Euler solved the “Seven Bridges of Königsberg” — proving you COULDN’T cross all seven bridges once; it launched a whole field of maths.
✅ Quick check: To trace a shape without lifting your pen, it helps if how many dots have an ODD number of lines?
Say your answer out loud first — then reveal.
Zero or exactly two — Euler’s rule; more than two odd dots and it’s impossible to trace in one stroke.
The count of odd-degree nodes decides whether a one-stroke path exists.
🧪 Try it! (2 minutes)
Try to draw an envelope shape (□ with an X on top) without lifting your pen. Count the odd dots first.