Count the number of triangles in the picture above.

**Hint:** The answer is not 4. There's a faster way than simply counting them all!

Joey has an infinite number of identical books that are rigid and perfectly rectangular. He places them all in a stack on the edge of a table.

What is the maximum distance (parallel to the ground) that the edge of the top book can get from the edge of the table without falling over?

**Assume** the gravitational field is vertical and uniform.

\[ \begin{array} {cccc} \large & & \color{red}C & \color{blue}A & \color{green}R \\ \large & & & \color{red}C & \color{blue}A \\ \large + & & & & \color{red}C \\ \hline \large & & \color{blue}A & \color{green}R & \color{red}C \end{array} \]

If \( \color{red}C\), \(\color{blue}A\), and \(\color{green}R\) are (not necessarily distinct) non-zero digits, what is the 3-digit final sum \( \overline{ {\color{blue}A} {\color{green}R} {\color{red}C } }? \)

**distinct** positive integer. Is it possible to fill in the circles such that each pair of adjacent circles adds up to a prime number?

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