Ask Math Anything Topics from May 2020

debbie

Tue 5/12/20 Live stream topics

Let \(a\) and \(b\) be any positive integer such that \(ab + 1 \) divides \( a^2 + b^2\). Show that \( \frac{a^2 + b^2}{ab + 1}\) is the square of an integer. Are \(a\) and \(b\) even?
What are some good ways to speed through mental math?
If \(a - b = 1\) and \(b-c = 1\) and \(c-a = 3,\) and \(abc = 60,\) what are \(a, b,\) and \(c?\)
99 in base 10 + 77 in base 10 equals what in base 9?
FOIL explanation with area
Is math related to Minecraft?
Once I assign mass points, what do I do after?
Let \(S\) be the set of all positive integers between 1 and 2017, inclusive. Suppose that the least common multiple of all elements in \(S\) is \(L.\) Find the number of elements in \(S\) that do not divide \( \frac{L}{2016}\)

debbie

Wed 5/13/20 Live stream topics

How many digits are there in \(100!\)?
What is \( 2!!!^{2!!^{2!}}\) ???
\(2^{2^{2^{2^{2^2}}}}\)
How do you stay motivated to work on math when times are difficult and your interest is fading?
Is it possible to make a checkerboard with one penny on the first square, two pennies on the second square, three on the third, and so on and so forth?
What is the smallest whole number that is equal to seven times the sum of its digits?
What's the best strategy to get far in the AMC's?
What's the number of edges in a 10-dimensional cube?
Why are there commas between every three digits in a number?
How many squares are there on an 8x8 chessboard?
Tips for learning calculus

debbie

Thu 5/14/20 Live stream topics

Tips for doing the countdown round at MATHCOUNTS
If there are two types of people, people who lie and people who don't lie, and you meet a stranger, how can you tell if they are a liar or not?
How to find the square root of a number manually

debbie

Fri 5/15/20 Live stream topics

Lexington Math Tournament Review
#1, #2, #7, #12, #28

debbie

Sat 5/16/20 Live stream topics

How do you cope with coronavirus? Do you go to the store on a daily basis?
The danger of coronavirus is that people spread it before they know that they are sick
Have you ever met Sal Khan, Richard Rusczyk or Terence Tao?
What kind of phone do you have?
Can human beings approach the speed of light?
Is NOVID going to be able to be sold?
Can you turn the blue background off and show us the green screen?
Have you ever met Grant Sanderson?
If you have never seen a type of problem, how do you approach it first?
What is the best way to learn? Like, how long should you learn, practice, research and rest? Thanks!
Why do you love math so much?
What do you do in isolation?

debbie

Mon 5/18/20 Live stream topics

Can music help with math? If so, then how?
Using math to win in monopoly
If you're flipping an empty bottle (like a Pure Life bottle), what angle do you need to throw it at in order to make it land on its cap?
Is it possible to have 3 real, distinct, non-zero numbers \(a, b,\) and \(c\) such that \(a, b\) and \(c\) form both an arithmetic and geometric sequence?
Geometric mean
What can be done to make education free for everyone globally? And make the world a better place?
We say \(\pi\) is an irrational number. That means it can't be expressed as \(\frac{p}{q}.\) But then why is \(\pi\) the ratio between the circumference and the diameter of a circle?
How to prove \( \sqrt{ab} \leq \frac{a+b}{2}?\)
If I give you a normal paper and tell you to fold it 30 times, can it be higher that the Himalayas?
How good are you at physics?
Can you prove that \(e^{\pi}\) is greater than \(\pi^e\) without using a calculator?
Why do you use Linux? Assuming it's good, how?
How accurate is sample size?
Are you the US National Olympiad coach?

debbie

Tue 5/19/20 Live stream topics

Conic sections
What is the probability that a person scores zero marks in a multiple-choice question test with 50 questions, each of which has 3 choices and gets three correct?
Is engineering more math or more physics?
Is luck real?
A special coin to explain math
What's your tips for improving math skills for a disciplined, non-math student?
Can you use math to win rock paper scissors?
What is as light as a feather but something the strongest animal or human can't hold?
How many vertices does a cube have? Euler's Polyhedral Formula
Is 4-D chess possible?
Why is the AMC logo an icosahedron?
Where did you learn to draw an icosahedron?
What's the best way to memorize something?
If you didn't do math, what would you major in?
What's the point of radicals?
Do you like art?

debbie

Wed 5/20/20 Live stream topics

The millennium prize problems
Could you please help us understand the values of negative \(n\)?
What was that ringing in the background?
Given \(n\) married couples, how many ways are there to form pairs consisting of one man and one woman who are not a couple?
Any tips for solving combinatorics problems generally?
Can you recite \(\pi\) to 100 digits?
What is your guidance for students who want to pursue research in math in the future?
If I don't like math, should I continue doing it?
I like non-routine math, but it takes time, and school doesn't allow that!
Why is math related to coding?
Do you think that one day, calculus will be taught in elementary school?
Could you explain the connection between sine in triangles and sine in waves and phenomena like sound?
Can you give some tips for solving geometry problems?
Do waves actually look like the sine function?
Is it possible to make a super fast bicycle using gear ratios?
Is it possible to make a super SLOW bicycle using gear ratios?
Is it possible to multiply \(\pi\) with an integer and get a rational number?
\( \frac{17}{21} \) vs. \(\frac{43}{50}\)

debbie

Thu 5/21/20 Live stream topics

Area of an equilateral triangle
Fraction of area used up by cookie dough if cookie are cut out of a rolled-out sheet of dough
In how many ways can we arrange a six-digit number such that it is non-decreasing?
Are there more irrational numbers or rational numbers?
How do you prove Heron's Formula?
Are there more composite numbers or prime numbers?
How can we find the radius of three circles with a triangle making a point at each center, where the triangle sides are 16, 18 and 20?
\( (A-X)(B-X)(C-X) \times \ldots \times (Z-X)= ?\) (MATHCOUNTS Countdown Round)
What is your key piece of advice for succeeding in Calculus, or any complex mathematics study?
Do you have a floating keyboard?
What is the probability of getting a perfect score on the SAT by guessing every answer?
How long did it take for you to code the program for this live stream?
Pick any number. If that number is even, divide it by 2. If it's odd, multiply it by 3 and add 1. Now repeat this process with your new number. If you keep going, you'll eventually end up at 1. Why?
If you know how to draw an icosahedron, do you know how to draw an icosahenagon (with 21 sides)?

debbie

Fri 5/22/20 Live stream topics

Mustang Math Tournament

Why is \(\sqrt{2}\) so useful?

debbie

Sat 5/23/20 Live stream topics

How does COVID affect global warming?
How to make a very slow rocket
Do you have any number theory tips?
How tall are you in feet?
Is it possible that Star Wars or Star Trek could be real?
What stylus do you have?
Did you get a scholarship at Cambridge?
Can you please make a coding video or talk about some coding?
Why is number theory so hard?
Do you think stopping time is possible?
How long have you been a professor?
Where do you get working code?

debbie

Mon 5/25/20 Live stream topics

\( n^2 + 6n = x^2.\) Find all solutions for \(n\) if BOTH \(n\) and \(x\) are integers.
How to explain the fourth dimension
What's a good password that is unhackable?
What is 1% of 2% of 3% of 4% of 5% ... of 100% of 10000?
Create a row of 6 squares. Place \(X, Y,\) and \(Z\) in the first 3 squares respectively. You have to move them to the last 3 squares only by moving letters one space to the right. Find the total number of ways to do this. (2017 CEMC Waterloo Caley Contest Problem #24)
3-D version of a Catalan number problem
Did you have a personal math teacher when you were younger, or did you study math on your own?
Are fingerprint passwords good?
How should I prepare for AOIME?
Do you have experience with machine learning calculus?
\( \frac{d}{dy} y^6 = 6y^5 \)

debbie

Tue 5/26/20 Live stream topics

Show that the next to last digit of \(3^n\) is always even.
The next to last digit of \(9^n\)
Binomial Coefficients and Pascal's Triangle
Have you looked at your Wikipedia page? Is the information there accurate?
Prove that powers of 5 have 2 as the second-to-last digit
How long would it take you to solve 6 IMO problems?
What is the smallest integer that you add to \( 2018 \times 2019 \times 2020\) to make it a cubic number?
If \( \frac{m+1}{m} = 9,\) then what is \(m^2 + \frac{1}{m^2}?\)
Prime factorize \(9991\) as the product of \(2\) primes
Have you ever met Eddie Woo?

debbie

Wed 5/27/20 Live stream topics

I have a broken calculator. If you type 39 it gives 12; if you type 98, it gives 17; if you type 54, it gives 92, and if you type 28, it gives 11. What does 53 give?
Can you prove that the Earth is round when no matter how much you walk, it still looks flat?
If multiplication is repeated addition, what does \( 0.1 \times 0.1\) mean in those terms?
How would the world be different if sound were at the same speed as light?
What is a probability that here on the chat there are two people who have the same birthday?
A large cube that is 5 cm by 5 cm by 5 cm, is painted orange on all six faces. Then it is cut into 125 small cubes, each 1 cm by 1 cm by 1 cm. How many of the small cubes are not painted orange on any face?
Three points, O(0,0), A(21,0), and C(0,21) are in a Cartesian coordinate system. Find the number of points interior of triangle OAB having only integer coordinates.
Pick's Theorem and the area of a triangle
Why are there so few girls in math and science?
Is NOVID going to be on Microsoft soon?
Let \(n\) be a positive integer. Construct a set of \(n\) consecutive positive integers that are not prime. Are there ten consecutive composite numbers?
Let \(a = \text{LCM} (2, 3, 4, 5, 6, 7, 8, 9, 10, 11).\) Then a series of consecutive composites are \(a + 2, a + 3, a + 4, \ldots, a + 11\)

debbie

Thu 5/28/20 Live stream topics

There are 30 students in a class. Carlos made 13 errors and all other students made fewer errors. Show that at least three students made the same number of errors.
Pigeonhole Principle
1729 as the sum of two cubes (\(10^3 + 9^3\) and \(12^3 + 1^3\) )
Simplify \( (a-1)(a+1)(a+2) - (a-2)(a+1)\)
How do you tell if a fish has gone bad?
If \( \text{gcd} (a,b) = 1,\) does this determine \( \text{gcd}(a,2b)\)
How to make \(147\) using four \(4\)'s
Factor this expression: \(24 v^2 + 10v - 6\)
How do you find the average of \(\frac{-5}{3} \) and \(-4\)?
What is the Collatz Conjecture?
Do you have a mask?
How to spend money wisely
What's the formula for the sum of triangular numbers?
Hockey Stick Identity
Can you use math to make a good meal?

debbie

Fri 5/29/20 Live stream topics

There are \(99\) little \(2 \times 2\) squares cut out of a big \(29 \times 29\) square. Prove that it is always possible to cut out one more \( 2 \times 2\) square from the big square.
What is the base \(5\) version of 110010? (110010 is in base 10)
Change 314159 to base 7
My parents need a new WiFi router; which one should we get?
The numbers obtained by only using the digits \(1, 2,\) and \(3\) are written in ascending order: \(1, 2, 3, 11, 12, 13, \ldots.\) What is the 2022-th number in this sequence?
What is the 930th number with 7 digits in 1, 2, 3?
Why not monetize your channel?
How do you get a life?

debbie

Sat 5/30/20 Live stream topics

Did you see the Space X launch? Do you think this will change the world?
Do you think celebrities get mobs of fans at their house?
How do I prepare for AOIME?
Why am I getting alerts from NOVID?
Which would you choose, pizza or taco or hot dog?
Do you guys have mobs of people at your office?
Opinions on Dyson spheres (huge megastructures that completely cover the sun and can harness its power)
What do you think every human being should achieve in life?
How many people have downloaded NOVID so far?
What's your least favorite subject?
Does learning a language help you in the future?
Can you talk about how you came up with the idea of building NOVID?
How to get better in math?
If you could make any other app, what would you make?