Can you always win 2048?

My intuition and experience tells me that, with optimal play, you can almost always — but not always — win 2048.

2048 is a wonderful puzzle game that I’ve spent far too much time playing (although probably not as much as what it’s based on, Threes.) 
I’ve never done real proofs in my life, but I know that to prove that you can always win, I need to prove that a malicious and omnipotent computer cannot defeat you.

I’ll assume you know how the game works. The rules that are most likely to end your game are: Continue reading Can you always win 2048?

A wild summer of re-exploring California

This summer, I was on a mission: to take photos, hang out with friends and family, and have fun in general before med school consumes my life. Now, one week before I fly off to New York I must say… MISSION ACCOMPLISHED!!

Two months, 29 days (50%) with significant shoots, 4000 snaps, 650 shots developed, 3000+ miles on the road, so many great memories. Sit tight, and let your computers buffer up, because this is a big post!  Continue reading A wild summer of re-exploring California

The absurd 64-mile bike ride

So yup, I biked 64 miles around Santa Barbara and it’s neighboring cities, along the beaches, through the foothills, downtown, uptown, through a mountainside neighborhood, and then some. It took 5.5 hours. I purportedly burned 2200 calories. It was longer than my previous longest two bike rides combined (37 mi and 26 mi), and I kind of can’t believe I pulled it off. Continue reading The absurd 64-mile bike ride

piano, photos, prose, photons