# Hatty Mary's Big Oops!

One day Jenny Chen received a coded message from Mary and instantly became both confused and amused. Jenny tells it this way.

Listen to the audio version.

"You see, Hatty Mary had just learned that you could use multiplication to encipher, so her message indicated to me that she had doubled the position numbers. Part of the message read

2 MC MC...

"The first number indicated multiplication by two. Oh no! No one had told Mary yet that she shouldn't use certain numbers as multipliers. I analyzed the message in this way:

• The cipher letter C has position #2;
• And 2 is twice #1, which is B;
• but there are no two-letter words that end in B.

"What I did was take C's position number, 2, and divided it by 2 to get B's position number, 1.

"Smith, can you think of any two-letter words that end in B? I had to look for another possibility.

"What other number could be doubled to result in 2(mod 26)? I worked it out to be 14.

"Mary must have doubled 14, which is letter O.

"Using doubling, Mary had caused a problem because both B and O encipher as the letter C in the ciphertext.

"The other cipher letter, M, has two possible origins also. One is G at position 6, which when doubled gives 12 and M."

 Value: 1Encipher the letter F at position 5 by doubling. Value: 1Encipher S at position 18 by doubling.

Agent Smith, using mod 26 arithmetic, can you figure out the other letter that would be enciphered as M? (Scroll down and hover of the word Hint for a tip.)