showboat algebra (n.)

 A blathering mess of algebraic manipulations that seem like a student attempted to find a solution to a particular homework problem.  After a few lines of incomprehensible scribble, the quality of the student's handwriting decreases to a minimum threshold after which the showboat sinks and the manipulations immediately resolve to the solution in the back of the book with no relation to previous steps.

EX:

<problem statement>
<bullshit>
<bullshit>
<bullshit>
<kinda true but still mostly bullshit>
<right answer from the back of the book that has absolutely nothing to do with what the previous step was>
*EX courtesy of Mary

"Maybe Walter Rudin could see air, but the rest of us keep walking into inappropriately placed glass walls."
"Wtf, was Walter Rudin a Mr. Mime?"

Budget or limited-service are such a better deal than more expensive hotels.  Let's just look at some of the details:

1. Price

"Nice" hotel: $200+/night
Budget Hotel: less than $100/night

2. Internet

"Nice" hotel: you pay for access daily
Budget hotel: free wi-fi!

3. On the house

"Nice" Hotel: Soap, towels, shampoo, complementary toiletries
Budget hotel: all that and FREE continental breakfast if you wake up for it.

So yeah, I gotta admit.
Nice hotels are ripoffs.



L

If four people are participating in a gangbang, one person will get stuck trying to fit n+1 pigeons into n coops.

My boss presented this problem to me and after solving it, I'm passing it on to you.

Mod-3 Solitaire

Take a standard deck of 52 cards, shuffle them, and then draw three cards from the top of the deck.  Lay them out in the order you drew them from left to right.  If there is an ACE in the first position, a TWO in the second position, or a THREE in the third position, then you lose.  If not, then set the cards aside and draw three more cards until an ace appears in the first position and so on (note that if you make it that far, the last draw in the deck will only consist of one card).  If you make it through all the cards and the deck without losing, then...obviously, you win!

The question is, what's the probability of winning the game?

A mathematician's daughter is turning 16 this month and she wants a new car for her birthday. The mathematician proposes that she may have a new car if she can solve the following puzzle:

Dearest Daughter:

Since you are turning 16 this year, I present to you the sequence {8,4,0,-2,-2,-1,0,1/2,1/2,1/4,0,...}. There is an additional 8 in this sequence which precedes all of the rest. This sequence somehow encodes the number 16. If you can extract the number 16 from this sequence, I will buy you a new car for your birthday. There are however, a few rules:

1.) The solution involves infinitely many members of this sequence.
2.) If the solution involves the nth term of the sequence, it must also involve the (n+1)th term.

The mathematician daughter has hired you to solve this problem for a substantial fee.
Can you propose a solution?

I'm going to start posting these little math puzzles. There's no prize or anything (yet) but they could be fun, so you should try to figure them out :)


March Math Puzzle: Avoid Bad Words!

In an arbitrary alien language, it just so happens that every curse word transliterates into the English language such that it contains an even number of the letter "A."

Note that a word of length zero vacuously contains an even number (0) of the letter "A." There is a single word of length zero (no characters whatsoever).

Now consider words of length 1. If the word is "A", then it does not contain an even number of As so it's not a curse word. But if the word is any other letter, then it contains 0 As, which is an even number of As, and since there are 25 other letters from which to choose, there are 25 curse words of length 1.

(1.) Find a formula for the number of possible words of length n, where n is the length of the word after transliteration into English, which are considered to be curse words in this alien language. The formula should be a function of the length of the word, and should work for n > 0.

In the same alien language, there are words which seem to have some sort of magical powers. It just so happens that every one of these words transliterates into English characters such that it contains an even number of vowels (A,E,I,O,U).

(2.) Find a formula for the number of magic words of length n, where n is the length of the word after transliteration into English, in this alien language. The formula should be a function of the length of the word, and should work for n > 0.

Notice that if a word happens to be a swear word and contains no other vowels, then it also is a magic word. In this language, these are considered to be a special class of words with evil effects when uttered.

(3.) Write a formula which gives the percent of curse words of length n which are also evil words.

Despite the ridiculousness, this *is* an extremely fast modular exponentiation algorithm.

#Missy Elliot Modular Exponentiation
#Computes a^b mod c via exponentiation by squaring
#Just, in a more humorous manner than usual
#Author, Kai Seward 2010 (for Python 3.1)

#produces a list of binary bits of a number
#but i'm kind of a bad programmer so it's backwards
def breakitdown(n):
	steps = []
	while n:
		steps.append(int(n % 2))
		n = n // 2
	return steps

#is it worth it? let me work it.
#shit's backwards, so i need to reverse it.
def putmythangdownflipitandreverseit(n):
	thang = breakitdown(n)
	thang.reverse()
	return thang

#compute a^b mod c via exponentiation by squaring
def modexp(a,b,c):
	workit = 1
	for thangs in putmythangdownflipitandreverseit(b):
		workit = (workit**2) % c
		if thangs:
			workit = (workit*a) % c
	return workit

I wish I had auto-tune for everyday life.
It would make classes 1337% more entertaining.

Autotune["Is the CONVERSE of this THEOREM true? GENERALLLYYYY NOOOOOOO!"]

One day President and Mrs. Coolidge were visiting a government farm. Soon after their arrival they were taken off on separate tours. When Mrs. Coolidge passed the chicken pens she paused to ask the man in charge if the rooster copulates more than once each day. "Dozens of times" was the reply. "Please tell that to the President," Mrs. Coolidge requested. When the President passed the pens and was told about the rooster, he asked "Same hen everytime?" "Oh no, Mr. President, a different one each time." The President nodded slowly, then said "Tell that to Mrs. Coolidge."