Early bird questions

Hi everyone, if you have a math question you would like to ask Prof. Loh, you can ask it here and we'll save it for the live stream!

Are curved functions like for example in a facing up U shape linear, always increasing, always decreasing, or something else?

This is a question I asked before as Vera Weng, and here is it:
Bob the had learnt to change his colours!
Every second, he have a 30% chance of not meowing, 40% chance of meowing once and 30% chance of meowing twice.
Every 5 meows he have a 40% chance of staying the same and 60% chance of changing into the next hue in the rainbow. (ie red to orange, blue to indigo etc)
If he started coloured red, what is the probability that it will end up green in one minute? 
Bob the cat best cat

@TheDarkinBlade Agree

They facts

@debbie Please log this one in!
There is a tendigit number with the property: the top digit is divisible by 1, the 2 top digits are divisible by 2, and so on, until the top 10 digits are divisible by 10.
Each digit in the tendigit number is unique.
What is the number?
(Warning: this probably came from a maths competition and the maths competition is probably AIME. But you don't have to be super good at maths to solve it. A fifthgrader like me can solve it.) 
@RZ923 Oh wow, thank you! I remember logging your question earlier. I think I know which username you were using for the live chat. I'll make sure to log it for tomorrow. Thank so much for coming, and have a nice day!

@debbie My username for the live chat is Vera Weng, my mum’s account.

@RZ923 Your patience has won out! Prof. Loh answered your question today (6/24/20) around 4:30 p.m. EST


@RZ923 My question is in there!

I promised Ethan Cao that I would put his/her question in here
"DO MY PROBLEM!!!!!!!!!! Mimi memed a meme. Mimi's mommy memed the meme that Mimi memed. Mimi's mommy's mommy memed Mimi's mommy's meme which was memed by Mimi. Is this a meme?"

@debbie This is not a meme but a tongue twister.

Last time I checked meme was just a noun?

@TheBladeDancer Yes it is a noun but memed(to spread memes) is a verb.

@debbie Zeno of Elea: (from aops intro to algebra) Suppose you wish to walk across the street. To get to the other side, you must go half of the way across the street. But first, you must walk halfway to the point that is half of the way across the street. But before that, you must walk halfway to the point that is a quarter of the way across the street. And before that, you must walk halfway to the point that is one eight of the way across the street. And so on forever. Because there are an infinite number of steps you must take to cross the street, you cannot cross the street.
How do you cross the road then?

We wake up from our illusion and cross the street for real.

@divinedolphin
Because it said “How do we cross the road“, not “How do we cross the street“, we go away from the street to a road and cross that road in one go.

Haha I'm not going to change it.