Level 6: Logic machines and networks

Logic and puzzles · level 6 of 8 · rough age 13-14 (a guide for parents; anyone can start anywhere)

Logic is not only for arguments: it can be built. In this level and, or and not become electronic gates that add numbers, and an algebra that simplifies circuits. Then you write exact step-by-step instructions (algorithms), count how much work they take, and meet search and sort methods that beat the obvious ones by huge margins. The level ends with networks: Euler's bridges and the four colour theorem.

Lesson	You will be able to
Logic gates	Use AND, OR, NOT, XOR and NAND, find the truth table of a circuit, and build a half adder that adds two bits
Boolean algebra	Use the laws of Boolean algebra to simplify expressions, and build every gate from NAND alone
Algorithms and flowcharts	Write precise algorithms and flowcharts, trace them, prove they work, and count their steps
Searching and sorting	Use linear and binary search, explain why 10 guesses find a number up to 1000, and sort by bubble sort and merge sort
Networks and Euler paths	Turn a map into a graph, decide whether a figure can be drawn in one stroke by counting odd vertices, and explain Königsberg
Graph colouring and maps	Colour graphs and maps with few colours, show when more are needed, solve timetable problems, and tell the story of the four colour theorem

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