Find a Green Triangle's Weight in a Balanced Mobile
Company: Sig
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Online Assessment
# Find a Green Triangle's Weight in a Balanced Mobile
A balanced hanging mobile weighs 160 pounds in total. Treat every horizontal bar as massless with equal-length arms, so the total weight hanging from its left side equals the total weight hanging from its right side. This equal-arm convention is an explicit practice assumption because the captured source describes the topology without arm lengths.
The top bar has a sub-mobile on its left and another assembly on its right. Within the left sub-mobile:
- its left side holds one orange octagon and one pink pentagon;
- its right side holds a second balanced bar;
- the second bar's left side holds a third balanced bar, while its right side holds one gray octagon and one pink pentagon;
- the third bar's left side holds a balanced bar containing two purple hexagons, while its right side holds one green triangle.
Find the weight of one green triangle in pounds. Express the answer as an integer. Show how balance at each nested bar determines the total weight above it; individual weights of the other shapes are not required.
### Clarifying Questions to Ask
- Are all bars massless and are their two arms equal in length?
- Does the stated 160-pound total include every hanging shape but exclude the bars?
- Does “a bar containing two purple hexagons” mean its total hanging weight is the sum of those two shapes?
### What a Strong Answer Covers
- Equal side weights at the 160-pound top bar, making each complete side weigh 80 pounds.
- A variable for the green triangle and upward propagation of whole-submobile weights.
- Recognition that a balanced bar's total weight is twice either side's weight.
- A derivation showing that the top-left sub-mobile weighs eight green triangles.
- The exact integer result with a check against the total weight.
### Follow-up Questions
- Why can the right side of the top mobile be ignored after establishing its total weight?
- How would the equations change if arm lengths were unequal but known?
- Which additional measurement would be needed if the bars themselves had nonzero weights?
Overview: Solve a nested balanced-mobile puzzle and determine the green triangle's weight from a 160-pound total. The worked derivation uses an explicit equal-arm, massless-bar assumption, propagates whole-submobile weights upward, and explains why the left branch alone fixes the answer at 10 pounds.
Read the full Sig Data Scientist interview experience this question came from