Find a Green Triangle's Weight in a Balanced Mobile

A balanced hanging mobile has a total weight of 160 pounds. Assume each horizontal bar is massless and has arms of equal length, so the weight suspended from its left side matches the weight suspended from its right side. This equal-arm rule is stated as a working assumption because the original description gives the layout but not the arm lengths.

The top bar carries a sub-mobile on its left and a different assembly on its right. Inside the left sub-mobile:

• the left side supports one orange octagon and one pink pentagon;
• the right side supports a second balanced bar;
• the second bar's left side supports a third balanced bar, while its right side supports one gray octagon and one pink pentagon;
• the third bar's left side supports a balanced bar holding two purple hexagons, while its right side supports one green triangle.

Determine the weight of a single green triangle in pounds. Give the answer as an integer. Show how the balance condition at each nested bar fixes the total weight hanging from it; you do not need the individual weights of the other shapes.

Clarifying Questions to Ask

• Are all bars massless, and do both arms of each bar have the same length?
• Does the 160-pound total count every hanging shape but not the bars themselves?
• Does "a bar containing two purple hexagons" mean the bar's total hanging weight is the sum of those two shapes?

What a Strong Answer Covers

• Equal side weights at the 160-pound top bar, so each full side weighs 80 pounds.
• A variable for the green triangle, with whole-submobile weights propagated upward.
• The observation that a balanced bar's total weight is twice the weight on either side.
• A derivation showing the top-left sub-mobile weighs eight green triangles.
• The exact integer answer, checked against the total weight.

Follow-up Questions

• After its total weight is known, why can the right side of the top mobile be set aside?
• How would the equations change if the arm lengths were unequal but known?
• What extra measurement would be needed if the bars themselves had nonzero weight?

Overview: Solve a nested balanced-mobile puzzle and find the green triangle's weight from a 160-pound total. The derivation assumes equal arms and massless bars, propagates whole-submobile weights upward, and explains why the left branch alone sets the answer at 10 pounds.