So basically 48 divided by 2 to the fourth power, which is 3 lbs.
Model the mobile as a binary tree where each split divides the total weight equally between the two branches. Since one side continues branching and the other terminates as a leaf at each level, the leaf at each level receives half of the weight that reaches that level. Calculate the weight at the bottom leaf after 4 levels by repeatedly halving the total weight.
Pro tip: Clarify the assumption that the mobile is perfectly balanced and that the branching side carries the remaining weight. This shows attention to detail and prevents misinterpretation.
Visualize the mobile as a binary tree where each bar splits the weight equally between its two sides. One side continues branching, while the other side ends in a leaf at each level.
At each level, the total weight is halved between the two sides. The leaf on the terminating side receives half of the weight at that level, and the remaining half goes to the branching side.
Compute the weight of the leaf at each level: Level 1 leaf gets 24 lbs, Level 2 leaf gets 12 lbs, Level 3 leaf gets 6 lbs, Level 4 leaf gets 3 lbs.
After 4 levels of halving, the leaf at the bottom (Level 4) weighs 3 lbs.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.