A challenging investigation into when a game is fair, using probability, and systematic search/algebra.

*This problem is based on a question asked by Doug WIlliams at the 2003 ATM Conference in Bath.

• Conditional probability
• Comfort with quadratic and muti-variable expressions
• Knowledge of how to create formulas in spreadsheets if using computer method.

Check the teacher sheet to decide on your approach. There are two possible approaches in question 3, you may choose to leave it open for pupils, or guide them as to one approach.