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.
134223142441313345414551423313
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 to...lol.
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.
No comments:
Post a Comment