Monday, February 27, 2012

Guess what I did today...

Guess what.

I just finished and submitted my Grad school application! It's done! It's now in the hands of everybody but me! Ahh!!!! Crazy.  But good. :)

On another note, want to know the math problem we worked on today in Combinatorics? It's a good one.


Okay, that is a 30-digit number made of the digits {1,2,3,4,5}

How many of that kind of number (30 digit # made from those 5 digits) have no adjacent 1's?

That's the problem we worked on.

It took lots of problem solving and prodding and probing.

It took us about 45 minutes and the help of a computer program once we figured out a recurrence relationship to feed the computer. (Translation: we figured out how many 1 digit, 2 digit, 3 digit and 4 digit numbers there are that are made of those 5 digits, with no adjacent ones, and then figured out a way to use those numbers to figure out the answer for all possible number lengths. We told it to the computer and it spit out the answer for a 30-digit number.)

Want to know the answer? I know you're dying

There are 336625345040561995776 numbers that are 30 digits long with no adjacent 1's. That's a 21-digit number... that's a huge number. Wow.

That's my day. :) Ah, the life of a math major.

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