Chandelier Balancing

By John Toczek

Constructing a chandelier can be a tricky undertaking because the slightest imperfection will unbalance the chandelier and cause it to be skewed.

Figure 1 shows a chandelier constructed from arms, wires and triangles that hold weights. In order to perfectly balance the chandelier, weights must be placed into the triangles. There are nine weights as follows: 1, 2, 3, 4, 5, 6, 7, 8, and 9kg. Each triangle can only hold one weight. Assume the weight of the arms, wires and triangles are negligible.


Figure 1. Balancing act: Where should the weights be placed?


Where should the weights be placed in order to perfectly balance the chandelier?

Send your answer to by April 15. The winner, chosen randomly from correct answers, will receive an “Analytics - Driving Better Business Decisions” T-shirt. Past questions can be found at

John Toczek is the director of Decision Support and Analytics for ARAMARK Corporation in the Global Risk Management group. He earned his bachelor’s degree in chemical engineering at Drexel University (1996) and his master’s degree in operations research from Virginia Commonwealth University (2005).