Logic, patterns and constraints

Recognise the model, justify the rule and solve independently.

Rewrite each statement as a condition that can be tested on one possible arrangement.

Use a table to eliminate options in a one-to-one matching, and justify each confirmed match.

Find a quantity that no allowed move changes, and use it to show that a target cannot be reached.

Prove a minimum in two parts: give an example that reaches it, and explain why fewer steps are impossible.