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Mathematics-Online problems:

Interactive Problem 98: Configuration of Pixels

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The figure shows some arrays of a $ 4 \times 4$-matrix of black and white pixels.

\includegraphics[width=0.25\linewidth]{TdM_10_A4_bild1}          \includegraphics[width=0.25\linewidth]{TdM_10_A4_bild2}          \includegraphics[width=0.25\linewidth]{TdM_10_A4_bild3}

How many different arrays exist having

(a) exactly one black pixel in each row and each column,
(b) at least 4 black pixels,
(c) exactly 4 black pixels joined together? (Each of the black pixels must have at least one side in common with another black pixel.)


Answer:

(a)
(b)
(c)


   

(From: Mathematics Contest 2010)
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  automatically generated: 8/11/2017