Kalshigood job Miguel
good job Miguel
Mitchieboi参与话题 50消息总数 4660
该用户的聊天记录定位。
聊天记录
共 4660 条，显示第 4301-4350 条YOURE SO BRAVE KATHY
YOURE SO BRAVE KATHY
yeah we've flipped to people being too loose with stink bids lmao
yeah we've flipped to people being too loose with stink bids lmao
kathy based for this
kathy based for this
hochul background
hochul background
https://tenor.com/view/everybody-hates-chris-everybody-hates-chris-meme-everybody-hates-chris-tv-show-everybody-hates-chris-boombox-boombox-gif-9984813089547523217
https://tenor.com/view/everybody-hates-chris-everybody-hates-chris-meme-everybody-hates-chris-tv-show-everybody-hates-chris-boombox-boombox-gif-9984813089547523217
kathy talking about why tech workers need to rto
kathy talking about why tech workers need to rto
they're collaborating more
they're collaborating more
nah
nah
helicopter ah parents
helicopter ah parents
like you don't need to have access to your kids during the day bro
like you don't need to have access to your kids during the day bro
yep
yep
like brother, kids went to school for hundreds of years without phones
like brother, kids went to school for hundreds of years without phones
and parents will do the "but what if my kids need to call me 😭 " shit
and parents will do the "but what if my kids need to call me 😭 " shit
a lot of schools do the phone lockers
a lot of schools do the phone lockers
but even then it's like
but even then it's like
if you've not gotten fcked before that point
if you've not gotten fcked before that point
I think 9th grade is a fine threshold to make it available
I think 9th grade is a fine threshold to make it available
sure
sure
and we'll talk about this like it was obvious
and we'll talk about this like it was obvious
it will be known that they cause insane ADHD
it will be known that they cause insane ADHD
but in 10-20 years
but in 10-20 years
we're not there yet as a society
we're not there yet as a society
like
like
phones are unequivocally TERRIBLE for kids dude
phones are unequivocally TERRIBLE for kids dude
yeah like
yeah like
but when she comes back she's wearing one of these. Does it count?
but when she comes back she's wearing one of these. Does it count?
say the livestream goes to intermission
say the livestream goes to intermission
what is a livestream btw
what is a livestream btw
i have never read them!
i have never read them!
what are these
what are these
sightseeing > WINE
sightseeing > WINE
sightseeing and WINE are tier 2
sightseeing and WINE are tier 2
https://open.spotify.com/track/0jV54uBrEZsd22ouECA3ts?si=18bf154047194b9f
https://open.spotify.com/track/0jV54uBrEZsd22ouECA3ts?si=18bf154047194b9f
this is the goat
this is the goat
fake fan
fake fan
And then the quadrants cases make it easy
And then the quadrants cases make it easy
Main thing is generalizing the problem to two points in a line
Main thing is generalizing the problem to two points in a line
But that's how I thought about it
But that's how I thought about it
If I drew it out it'd be super clear
If I drew it out it'd be super clear
So it's something like: 1. Recognize that the actual placement of the points is irrelevant, and that you can just imagine them as two points next to each other horizontally with some arbitrary distance between them. This is because any two points will connect a line, and the problem was "obviously" symmetric with respect to rotation and distance to me So just imagine two points next to each other 2. Now imagine drawing an infinite line out of the left point in one direction. It falls into one of four quadrants - up and right, up and left, down and left, down and right. Consider just up and right (towards the other point) and then think about the same four quadrants for the other point. Anything up and left would have to intersect (so fill that quadrant in) Anything up and right would intersect iff the slope of the right point's line is greater than that of the left's (the one we fixed). This has a 50% chance of happening via symmetry, so color "half of it in". Then the bottom ones obviously can never intersect. So we have 1.5/4 quadrants colored in, so when we fix the left point to top right quadrant, it has a 3/8 chance of happening. Apply similar reasoning to fixing the left point to the top left quadrant and find that it has a 1/8 chance. This averages to 1/4 for the top two quadrants on the left point. By symmetry, bottom two quadrants will be the same, so 1/4 total
So it's something like: 1. Recognize that the actual placement of the points is irrelevant, and that you can just imagine them as two points next to each other horizontally with some arbitrary distance between them. This is because any two points will connect a line, and the problem was "obviously" symmetric with respect to rotation and distance to me So just imagine two points next to each other 2. Now imagine drawing an infinite line out of the left point in one direction. It falls into one of four quadrants - up and right, up and left, down and left, down and right. Consider just up and right (towards the other point) and then think about the same four quadrants for the other point. Anything up and left would have to intersect (so fill that quadrant in) Anything up and right would intersect iff the slope of the right point's line is greater than that of the left's (the one we fixed). This has a 50% chance of happening via symmetry, so color "half of it in". Then the bottom ones obviously can never intersect. So we have 1.5/4 quadrants colored in, so when we fix the left point to top right quadrant, it has a 3/8 chance of happening. Apply similar reasoning to fixing the left point to the top left quadrant and find that it has a 1/8 chance. This averages to 1/4 for the top two quadrants on the left point. By symmetry, bottom two quadrants will be the same, so 1/4 total
Very neat problem
Very neat problem
Nice I was right
Nice I was right
Yeah it is 0.25
Yeah it is 0.25
There's a really nice visual proof if I'm right
There's a really nice visual proof if I'm right
Let me double check
Let me double check
It's 0.25
It's 0.25
Naively
Naively
But I THINK
But I THINK
I haven't looked at the answer yet
I haven't looked at the answer yet