In how many ways can you spell the word COOL in the grid below? You can start on any letter C, then on each step you can step one letter in any direction (up, down, left, right, or diagonal).

\[\begin{array}{ccccc}

C&C&C&C&C\\

L&O&O&O&L\\

L&O&O&O&L\\

L&O&O&O&L\\

C&C&C&C&C\\

\end{array}\]

flowiery Jul 21, 2023

#1**0 **

You can count the number of ways you can spell cool from the second $c$ on the top row and get $2$. Then $ 2 \cdot 4 = 8 $ because of the other $3$ c's. Then count how many was to make cool from the middle $c$ and you get $4$. Then $ 4 \cdot 2 + 8 = 16$ because of the other middle $c$.

Then you count the number of ways to make cool from the corner $c$ and you get $2$. Then $ 2 \cdot 4 + 16 = 24$ because of the $3$ other $c's$.

That gives you a total of $16 + 24 = 40$ ways.

Guest Jul 21, 2023