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Grade Vs Difficulty:

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Problem

Suppose we begin with a knight sitting at (1,0,0) in three-dimensional space. A $\textit{three-dimensional knight jump}$ is a move where a piece goes $\pm 1$ along one axis (i.e. in the $x$, $y$, or $z$-directions), $\pm 2$ along a second axis, and $\pm 3$ along the remaining axis. For example, our knight at (1,0,0) could make a three-dimensional knight jump to (1,0,0) +(2,-1,3) = (3,-1,3), or perhaps to (1,0,0) + (-1,-3,-2) = (0,-3,-2). Show that it is not possible for our knight to reach (0,0,0) by making a finite number of three-dimensional knight jumps.

Details
Source Title: Oakland/ East Bay Math Circle - Sept 17, 2007
Authors
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References
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Problem Sets This Problem Belongs to:
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VARIABLES
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DEFINITIONS
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