### Number Theory

On the first day of medical school, a professor writes her name on the board in a secret code:

$\huge\text{ES. TNJUI}$

What is the actual last letter of her last name?

The code used is called a "Caesar shift." Pictured below is a "decoder ring" used to encode and decode messages into and out of this code and a family of similar codes. In real life, the inner wheel of letters would spin independently of the outer wheel of letters.

# Secret Messages

Number theory plays a key role in encryption — the process of hiding and encoding information. Encryption enables the military to pass on messages secretly, merchants to pass credit card numbers to banks, and everyone to sign in (passwords) and check encrypted emails.

Numerical algorithms are one of the key ways engineers encrypt information. Algorithms turn messages into code that is impossible to read until the message is decoded.

# Secret Messages

The pigpen cipher replaces letters for symbols based on the grid below:

For example, the message "WORDS" encoded with the pigpen cipher is shown below.

What is the secret message encoded below?

# Secret Messages

A magic word is needed to open a certain box. A secret code assigns each letter of the alphabet to a unique number. The code for the magic word is $9 \ 23 \ 14\ 14\ 18\ 5.$ What could be the magic word?

# Secret Messages

In a certain code language, three messages are encoded as follows:

• Cats don't like apples $\Rightarrow$ pic sip dip rit
• Parrots really like apples $\Rightarrow$ dip pic tif nit
• Cats like parrots $\Rightarrow$ sip dip tif.

How is the word "don't" written in the code language?

# Secret Messages

To send a private message, Alan encodes it by rearranging the letters.

To do so, he first writes the word across two rows, switching between the top and bottom row with each letter, as in the sample below:

He then reads the message across each row, starting with the top one and then moving to the bottom. In this case, the word "SAMPLE" would become "SMLAPE" once it is encoded.

Alan sends the message "ATRNLEIG." What was his original word?

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