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problem:simple_shift_on_26_letters
This is an old revision of the document!
- This is currently just a stub. I will finish it up.
Long ago, in ancient Rome, Julius Caesar is said to have used simple ciphers
to encrypt messages that he wanted to stay secret.
The following problems are based on a modified version of this same cipher.
Caesar started by writing out the alphabet and pairing each letter to a number that would represent it.
One such pairing is
$$
\begin{array}{c|c|c|c|c}
a&b&c&\cdots & z\\\hline
0&1&2&\cdots & 25
\end{array}.
$$
With this pairing, we would encode the word defend as 4, 5, 6,
5, 14, 4. We'll call this the trivial pairing.
\begin{problem} I want them to come up with a definition for a pairing. Then I want them to encode a word using their pairing.
Then I will give them a pairing (a shift right of 3 units). Then from the pairing I gave them, I will ask them to decode a message.
\end{problem}
Comments
I would like them to realize that one of the key ideas for making a pairing work is that they need a function that has an inverse. This should make inverses become crucial.
They are basically starting with symmetric groups with this problem. I might ask them how many such pairings exist (26!), but I'm not sure.
problem/simple_shift_on_26_letters.1376198086.txt.gz ยท Last modified: 2013/08/11 01:14 by bmwoodruff
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