Solution

Encode the message "RUN AWAY NOW" with a Vigenere cipher using the keyword "YELLOW"


First, we write the letters of our keyword above the letters of our message (repeating the keyword as necessary), noting the appropriate values for each such letter $\pmod{26}$:

$$\begin{array}{cccccccccc} 24 & 4 & 11 & 11 & 14 & 22 & 24 & 4 & 11 & 11\\ Y & E & L & L & O & W & Y & E & L & L\\ 17 & 20 & 13 & 0 & 22 & 0 & 24 & 13 & 14 & 22\\ R & U & N & A & W & A & Y & N & O & W\\ \end{array}$$

Then, we add the shifts corresponding to the keyword letters to their matching values corresponding to the letters of our message $\pmod{26}$:

$$\begin{array}{cccccccccc} 24 & 4 & 11 & 11 & 14 & 22 & 24 & 4 & 11 & 11\\ Y & E & L & L & O & W & Y & E & L & L\\ 17 & 20 & 13 & 0 & 22 & 0 & 24 & 13 & 14 & 22\\ R & U & N & A & W & A & Y & N & O & W\\\hline 15 & 24 & 24 & 11 & 10 & 22 & 22 & 17 & 25 & 7 \end{array}$$

Finally, we reinterpret this last list of numbers as letters to arrive at our encrypted message:

$$15,24,24,11,10,22,22,17,25,7 \rightarrow \textrm{ PYYLKWWRZH}$$