An investigation of happy and sad numbers, uncovering a repeating cycle, and exploring why every digit-square sequence must eventually repeat.

• Square numbers
• Forming basic algebraic expressions

1. Read through the attached teacher sheet, and print off a copy for reference.

2. Explain the basic algorithm to pupils. After your explanation, and reading through the exam pupils will be ready to go.

3. Pupils will be ready to go after your explanation but section 4 - called, No Escape? - may warrant some class discussion.