roles) || in_array('administrator', $user->roles) || in_array('admin', $user->roles ) ) { ?>
probname); ?>
Topic Classification: nid, "Topic Classification"); ?> Tags: nid, "Problem Tag");?>
Topics: nid, "Topics"); ?> Prerequisites: nid, "Prerequisites"); ?>
Supplies: nid, "Supplies"); ?> Pedagogy: nid, "Pedagogy"); ?>
Grade Vs Difficulty:
  EasyModerateChallengingPerplexing
1-2
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5-6
 
 
7-8
 
9-10
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13-14
Solution: nid, "Solution"); ?>
Problem

We define a $\textit{(weak) magic square}$ to be a square matrix whose entries are nonnegative integers and whose rows, columns, and main diagonals sum to the same number.
Let $\left( x_{ ij } \right)_{ 1 \le i, j \le 3 }$ be a magic $3 \times 3$ square.

a) Show that the center term $x_{ 22 }$ is the average over all $x_{ ij }$.

b) Show that there are no magic $3 \times 3$ squares with line sum $t$, if $t$ is not a multiple of $3$.

Details
Authors
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References
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Reference Author Reference Title Reference URL
'; } ?>
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Problem Sets This Problem Belongs to:
parent_nid; ?> Set:
VARIABLES
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DEFINITIONS
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