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straints: • The penny starts at the point (1, 1) •From any point (i, j), the penny can move to (2i, j) or (i, 2j) • From any point (i, j), the penny can move to (i-j,j) if i > j, or to (i, j - i) if j> i. For which positive integers x, y can the penny be moved to (x, y). The statement should be an "if and only if", hence two implications must be proved.

straints: • The penny starts at the point (1, 1) •From any point (i, j), the penny can move to (2i, j) or (i, 2j) • From any point (i, j), the penny can move to (i-j,j) if i > j, or to (i, j - i) if j> i. For which positive integers x, y can the penny be moved to (x, y). The statement should be an "if and only if", hence two implications must be proved.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 18EQ
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15. A penny is moved in the cartesian plane according to the straints: • The penny starts at the point (1, 1) • From any point (i, j), the penny can move to (2i, j) or (i, 2j) • From any point (i, j), the penny can move to (i-j, j) if i > j, or to (i, j - i) if j> i. For which positive integers x, y can the penny be moved to (x, y). The statement should be an "if and only if", hence two implications must be proved.
Transcribed Image Text:15. A penny is moved in the cartesian plane according to the straints: • The penny starts at the point (1, 1) • From any point (i, j), the penny can move to (2i, j) or (i, 2j) • From any point (i, j), the penny can move to (i-j, j) if i > j, or to (i, j - i) if j> i. For which positive integers x, y can the penny be moved to (x, y). The statement should be an "if and only if", hence two implications must be proved.
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