Weighing a shape on a balanced mobile

Solving this mobile-balance algebra problem

This is a medium-difficulty constraint-satisfaction problem that tests your ability to set up and solve a system of linear equations under real-world structure constraints. It's the kind of question that appears in interviews for roles emphasising analytical thinking and careful logical decomposition—particularly at firms that value systematic problem-solving over pattern recognition.

The key skill is translating a hierarchical, physical system (a balanced mobile) into a set of algebraic equations. Since every crossbar is perfectly balanced, the weight on the left side of each pivot must equal the weight on the right. Shapes of the same type have identical weight, so you can assign variables and propagate constraints upward and downward through the tree structure. Success depends on correctly parsing the nested description, avoiding arithmetic errors, and solving the resulting system without losing track of dependencies.

• Constraint propagation through hierarchical structures
• Systems of linear equations with multiple unknowns
• Careful bookkeeping when parsing complex nested descriptions
• Verification by checking all balance conditions