Wednesday, April 20, 2011

EB: Cryptology

The first class we learned about the Caesar Cipher and other shift ciphers, as well as learning some useful cryptology words.
  • Plaintext - the meaningful English message
  • Ciphertext - what you actually send; the secret coded message
  • Encrypt - turn the plaintext into ciphertext
  • Decrypt - turn the ciphertext back into plaintext
The students paired off and sent their partners encrypted messages to decrypt.

Today I gave the class several encrypted messages to break, of increasing degrees of difficulty. We worked them all out on the board. It was helpful that I forgot what the plaintext messages were!

Here's the first one:

MJQQT, HQFXX.
HTSLWFYZQFYNTSX TS GWJFPNSL YMNX HNUMJW!
- OJXXJ

This one is pretty easy. It looks like a letter, and I wrote it, so "OJXXJ" stands for "JESSE." The first word, "MJQQT," is "HELLO." Since I used a shift cipher, the rest follows from there.

For the next message, I didn't give them any helpful formatting.

KXNDRSCYXOKVCYFOBIXSMO

The most common English letter is "E," and the most common characters in this ciphertext are "X" and "O." I was still using a shift cipher, so there were really only two things to try. That didn't take long either.

Then, since they kept breaking my shift ciphers, I changed to a cipher that randomly mixed up the letters. I did give them back the formatting, though - I didn't want it to be impossible (or take more than the hour-long class)!

VCPT PT E DPYYRHRNV VMSR FY ZFDR

The letter "E" in the ciphertext is a one-letter word, so it must be either "I" or "A" (assuming I'm using grammatical English!). The class went with "A".

Then the two-letter words in the ciphertext, "PT" and "FY," must translate to two-letter English words that don't contain the letter "A." Also, the two-letter word "PT" is the second half of the four-letter word "VCPT." It was agreed that "THIS IS" was a reasonable guess at those first two words.

From there, they got the answer!

The picture shows, from left to right:
  • The ciphertext-to-plaintext translation (we used this more for the first two puzzles)
  • The ciphertext, with plaintext underneath
  • A list of common 2-letter English words

Tuesday, April 19, 2011

More Killer Sudoku

Yesterday and today we worked on this puzzle. Renata and I were impressed with how well everyone worked on it - almost every moment was full of raised hands and kids saying "I know something!" We finished before the end of class!




Thursday, April 14, 2011

Origami and Pascal's Triangle

The first quarter of April was spring break, and we haven't had time to do a whole lot since then. We've made some neat origami vases and boxes. The vase required folding the paper exactly in thirds, so we had to figure out how to do that (Google "origami thirds" and you'll find several different ways).

We also did a little more stuff with Pascal's Triangle. If we left-justify all the numbers, we get a staircase instead of a pyramid:

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

If we sum the numbers in each row, we get doubles:

Sum
1 1
1 1 2
1 2 1 4
1 3 3 1 8
1 4 6 4 1 16
1 5 10 10 5 1 32

If we sum the numbers on each finite diagonal, we get the Fibonacci numbers. I think this is really cool.

Sum
1 1
1 1 1
2 1 2 1
3 1 3 3 1
5 1 4 6 4 1
8 1 5 10 10 5 1