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Analytics Magazine

Thinking Analytically: Frog and fly

July/August 2014

By John Toczek

Figure 1: Where will the frog dine on the fly?

A frog is looking to catch his next meal just as a fly wanders into his pond. The frog jumps randomly from one lily pad to the next in hopes of catching the fly. The fly is unaware of the frog and is moving randomly from one red flower to another.

The frog can only move on the lily pads and the fly can only move on the flowers. The interval at which both the frog and the fly move to a new space is one second. They never sit still and always move away from the space they are currently on. Both the frog and the fly have an equal chance of moving to any nearby space including diagonals. For example, if the frog were on space A1, he would have a one-in-three chance each of moving to A2, B2 and B1.

The frog will capture the fly when he lands on the same space as the fly.

Question: Which space is the frog most likely ?to catch the fly?

Send your answer to by Aug. 15. The winner, chosen randomly from correct answers, will receive a $25 Amazon Gift Card. Past questions can be found at

John Toczek is the senior director of Decision Support and Analytics for ARAMARK Corporation in the Global Operational Excellence group. He earned a bachelor of science degree in chemical engineering at Drexel University (1996) and a master’s degree in operations research from Virginia Commonwealth University (2005). He is a member of INFORMS.

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