House Robber and Boredom share a pattern: taking an element blocks its neighbors. This creates a "skip or take" decision at each position.
The general recurrence is . Skip position (keep previous best) or take position (add value to best from two back). Variations include: different blocking rules (block next instead of ), different values (constant vs variable), and reconstruction (tracking which elements were taken).
When you see a problem where taking one thing prevents taking nearby things, try mapping it to this pattern. The reduction often makes the solution obvious.