THIN K IN G A N A LY T I CA LLY
Frog and 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
Figure 1: Where will the frog dine on the fly?
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.
BY JOHN TOCZEK
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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QUESTION: Which space is the frog most likely
to catch the fly?
Send your answer to [email protected] by
Aug. 15. The winner, chosen randomly from correct
answers, will receive a $25 Amazon Gift Card. Past
questions can be found at puzzlor.com.
A N A LY T I C S - M A G A Z I N E . O R G
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