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'Robert's Spreadsheet' printed from https://nrich.maths.org/
Can you predict where $29^2$ will appear? Or $34^2$? Or
$52^2$?
Where are the odd square numbers?
Are there diagrams that could help you to show what happens when
you square an odd number (or an even number)?
By representing an odd number as $2n+1$, can you explain any of the
patterns in the odd square numbers?