Problem 2 · The balanced mobile
Each bar splits the weight in half: the star hangs after four splits.
Integer answer, at most 4 digitsThe figure shows a mobile in equilibrium. Ignoring the weights of the horizontal bars and vertical strings, the total weight is 112 grams. How many grams does the star weigh?
Copa Cangur · SCM
Medium
Closed answer
Reasoned solution
Key idea: in a balanced mobile with equal arms, each bar splits the weight it carries into two exact halves.
Follow the star's branch from the ceiling: the whole mobile weighs $112$ g; the main bar gives $56$ to the right side; the right bar passes $28$ to its right arm; that splits again into $14$, and the last bar shares $7$ and $7$ between the circle and the star.
$$112 \to 56 \to 28 \to 14 \to 7: \qquad \frac{112}{2^{4}} = 7\ \text{g}.$$
Answer: 7