@ask_ourself@yashkaf@TaterTotient Well, you do have to be a little careful about endpoints, since the proof requires two of them. E.g. you can go from 0% (0/2) to 66% (4/6) without crossing 25%, though you do cross 50%. The exact values in the OP prevent this. Still a very clever problem (I missed it as well).
A basketball player has a season free throw average of 70% halfway through the season, and raises it to 80% by the end of the season.
Is it necessarily true that it was exactly 75% at some point? Why or why not?
@ryanqnorth@tvaneerd@John71193784 1. You promised tweets, not a tweet.
2. You said "Jughead is". That makes it a present Jughead tweet, not a future Jughead tweet.
@ccanonne_@xkcd Unmumbling: Else we know that after one step two numbers are at most X_2/3 and the third is at most X_1. So after another step all numbers are at most X_8/9.
@ccanonne_@xkcd Let the numbers be (L,M,U) in increasing order. U-L shrinks by 1/9 every two steps: Let X_c=(1-c)L + cU for c in [0,1]. Use AM>=GM to see that two numbers in the next step are at most X_2/3. If M<X_8/9, enough shrinking happens. Else *mumbles*. ▫
@ryanqnorth Hey, I'm a huge fan of squirrel girl, but I think the latest issue has exponential written instead of quadratic. It's bugging me, is anything going to be done about it?
Thanks in advance.