Give a contrapositive proof: For every 2D table of blue and gray pebbles, if the total number of gray pebbles is at most the number of columns, then at least half of the columns are almost-blue. (Note: almost-blue is to mean the column has at most one gray pebble.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Give a contrapositive proof: For every 2D table of blue and gray pebbles, if the total number of gray pebbles is at most the number of columns, then at least half of the columns are almost-blue. (Note: almost-blue is to mean the column has at most one gray pebble.) Be sure to clearly explain.
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