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Write-up


Title
Breaking the Code 

Problem Statement

The most common letter used in the English language is E. The next most common is T. The vowels O, A, and I are the next most common; then comes the letter N. Code breakers (cryptologists) use this information to break simple substitution codes. In the sentence that follows, each letter stands for another. For example, the letter D stands for the same letter every time it occurs. Use what you know or can find out abut common letters to decode this message:

 

DMRA EXCEFX GC RCQ JRCL QBMQ QBX NQOGA CS DMQBXDMQTUN UMR BXFE QBXD WXMG CW LWTQX M UCGX.


Problem setup

I set up this problem by writing out the coded message with a blank line between each line of the sentence in order to have room to write the decoded letters above each coded letter.

 

Plans to Solve/Investigate the Problem

I decided to start with the lone letter M. I assumed it was an A, since the only other choice would be an I. I thought there was a higher probability that it was an A.

 

Investigation/Exploration of the Problem

After I first used A for M, I substituted it for every M. That led to an exploration of the two letter words such as GC, CS and CW. Since all of these two letter words contains a C, I thought of the two letter words and the letters they contain such as ON, TO, IS, IF, IN, DO, etc. I then looked at the three letter words RCQ, UMR and QBX. I assumed that one of those three letter words was the word THE. So, if one of those is THE, and the only two letter word I could think of that contains one of the letters in THE is TO, I then had to think of other three letter words. I thought of TOO, NOT, CAN, BUT, HAD. Since O came up several times in the three letter words, I assumed that it was present in the three letter words and in the two letter words. I made C the O since O is common in the two letter words I thought of and C is common in the coded message. So I made the letter C, O. This gave me OS, GO, and OW. I thought of ON, OF, SO, DO. I looked at the three letter words for further help. C was in the RCQ so now I had ROQ. I thought of NOT. I assumed this was the word. After plugging in all of these letters and substituting them in other places, I had more of the puzzle completed. I then had several Ts, and Ns. I guessed at THAT, THEM and the rest of the two and three letter words from there. I then tried to make words from what I had. Some of the words I chose were incorrect when I saw that they did not all fit together in the message. I even had instances where I used the same letter for two different coded letters. A big help was when I figures out that one of the words was PEOPLE which has two Es and two Ps. This was definitely a turning point. I could now see that the word MATHEMATICS was the big word in the message. Of course, why wouldn’t Intermath put the word Mathematics in a message on its website? This was a big help because of the number of letters. After substituting all of these throughout the message, I got the final message which is: MANY PEOPLE DO NOT KNOW THAT THE STUDY OF MATHEMATICS CAN HELP THEM READ OR WRITE A CODE.

 

Extensions of the Problem

From decoding messages, a math instructor may branch out into frequency tables, graphs, charts, probability, percentages.

Author and Contact
Pam Joseph
 


 

 

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