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Resonance

January 2003
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Classroom

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. “Classroom” is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science.

A Number-theoretic Game

Prithvi Ramesh

Consider any four natural numbers a, b, c, d and look at the
transformation (a,b,c,d) -> (|a-d|,|b-a|,|c-b|,|d-c|).

On performing repeated iterations, what do we observe?
For example, (1,3,7,15) ->(14,2,4,8) -> (6,12,2,4) -> (2,6,10,2) -> (0,4,4,8) -> (8,4,0,4) -> (4,4,4,4) -> (0,0,0,0) ...

Address for Correspondance

Prithvi Ramesh
BA Hons. Mathematics 3 rd Year
St. Stephens College
Delhi, India.

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Indian Academy of Sciences
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