- When Alice draws a 5-card hand from a deck of cards, she must get at least two cards of the same suit.
- Think of a deck of cards as going from 1 (ace) to 13 (king) and put these numbers around a clock. The farthest apart any two cards can be is 6 steps, so long as you start on the correct card (it takes 7 steps to get from 13 to 7 but only 6 steps to get from 7 to 13).
Tuesday, June 7, 2011
Mind-reading card trick
Monday, June 6, 2011
Cryptology - the final foray
- If there are prizes, they must be divided evenly.
- Cooperate! Help each other! Also, make sure everyone gets to help.
- Leave the room as you found it.
1. Easiest first! XQGHU WKH WUDVK FDQ
2. The mystery starts with AAA. AIHFACJQMBJOLYW
Catching up on the blog!
- A polyhedron is a 3-D object, as opposed to a polygon, which is a 2-D object.
- Regular in this case means "all the same." A regular polygon is a polygon where all the sides and angles are the same length, such as an equilateral triangle or a square. A regular polyhedron is one for which all the sides are the same regular polygon.
- A polygon or polyhedron is convex if, when we pick two points inside it and connect them by the shortest straight line, the line is entirely contained inside the polygon or polyhedron.
Friday, May 13, 2011
Creating Hydrogen and Oxygen from Water
This is a smaller scale experiment than what we did in class. This can be safely done at home, and will not involve the collection of the gasses.
Here are the items you will need.
1: Glass container (a jam jar works well here).
2: Two pencils
3: A piece of cardboard slightly bigger than the glass.
4: Two pieces of thin electrical wire about 8-10 inches in length.
5: Electrical tape.
6: Epsom Salt (this is NOT table salt. Ask your parents!)
7: A 9 volt battery.
Experiment steps:
1: Remove the erasers from the pencils and sharpen both ends.
2: Attach one wire (about 8-10 inches long) to each pencil by wrapping the exposed wire around one end of the pencil, and using the electrical tape to secure it.
3: Fill the glass container about 3/4 of the way with water.
4: Mix several tablespoons of the Epsom salt in with the water. You want to saturate the solution, so keep mixing until no more will dissolve. Do this about 1 tablespoon at a time.
5: Put the cardboard piece on top of the glass, and poke two holes about 2 inches apart. Push the end of each pencil that does not have the wire attached through the holes, and into the water.
6: Finally, attach the other end of the wire to the 9 volt battery with the electrical tape to help hold them in place.
At this point you will see bubbles forming at the tips of the pencils in the water. If you look closely, one will be forming bubbles more quickly than the other. This is the Hydrogen. The one with the fewer
bubbles is the Oxygen.
That's it! You have successfully split hydrogen and oxygen from water.
Wednesday, May 11, 2011
Cryptology - Enigma Machine
Cryptology - The Alphabet Clock
plaintext CHICKEN 2 7 8 2 10 4 13
key MOOFAZA 12 14 14 5 0 25 0
sum 14 21 22 7 10 29 13
Then we translate the numbers back into letters. On the alphabet clock, 29 and 3 are both D.
14 21 22 7 10 29 13
O V W H K D N
We send the ciphertext OVWHKDN.
To decrypt the message, we need to know the ciphertext and the key. Since we added the key to get the ciphertext, we have to subtract the key to get the plaintext. Translate the ciphertext and key into numbers, and take the difference between each pair of numbers:
ciphertext OVWHKDN 14 21 22 7 10 29 13
key MOOFAZA 12 14 14 5 0 25 0
difference 2 7 8 2 10 4 13
Finally we translate those numbers back into letters:
2 7 8 2 10 4 13
C H I C K E N
If the key is totally random and as long as the message, we have what's called a one-time pad. In one sense, this is the best cryptography there is: if you don't know the key, you can't figure out the message. I don't care how good your computer is - it can tell all the possible messages, but it can't tell which was the real one.
In another sense, this is horribly impractical. You have to get a gigantic list of completely random letters to your buddy, without anyone else seeing them, and you and your buddy have to always be at the same place in the gigantic list of letters. What a mess!
Wednesday, April 20, 2011
EB: Cryptology
- 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 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