Today's Topics (June 2020)

[The Blade Dancer]

Ooh can I go when you do infiltrate it

[debbie]

Topics from the 06/22/20 live stream

• Find the number of three-digit numbers such that the digits are in strictly increasing order from left to right. For example, $123, 489,$ etc.
• We have a suggested expression, $9 \times 9 \times 8,$ for the above question, which isn't actually correct. Let's try to find a question that would give $9 \times 9 \times 8$ as an answer!
• What would happen if all the water in a rainstorm came down in one huge drop? (It was raining hard )
• In the right triangle $\bigtriangleup ABC, AC = 12, BC = 5,$ and angle $\angle C$ is a right angle. A semicircle is inscribed in the triangle on side $AC$ at the right angle. What is the radius of the semicircle?
• Why is it named the Pythagorean Theorem?
• How many $0$'s does the base ten numeral $58!$ end with when written in base $12?$
• Which award is considered to be like an Oscar for math?
• How to find the volume of a banana
• What is Avogadro's Number?
• The area of a cuboid is $150 \text{ } \text{m}^2.$ What is the height of the cuboid if its volume is $1800 \text{ } \text{m}^3?$

[debbie]

Topics from the Tues 6/23/20 live stream

• If $k$ and $n$ are integers and $\left( 3^{2006} + 2006 \right)^2 - \left( 3^{2006} - 2006 \right)^2 = k \times 3^n,$ where $k$ is not divisible by $3,$ compute $\frac{n+k}{2006}.$

• What is the value of $\frac{2020^2 - 2012^2}{2017^2 - 2015^2}?$

• Do you consider yourself a mathematician, mathemagician, or math teacher/coach?

• The positive integer $n$ is between $1$ and $20.$ Milly adds up all the integers from $1$ to $n$ inclusive. Billy adds up all the integers from $n+1$ to $20$ inclusive. Their totals are the same. What is the value of $n?$

• Are eggs good for you?

• On an algebra quiz, $10\%$ of the kids scored $70$ points, $35\%$ got $80$ points, $30\%$ got $90$ points and the rest scored $100\%.$ What is the difference between the mean and the median of the students' scores?

[debbie]

Topics from the Wed 6/24/20 live stream

• The lengths of the sides of a triangle in inches are three consecutive integers. The length of the shortest side is $30\%$ of the perimeter. What is the length of the longest side?
• The base-3 repeating decimal $0.\overline{12}_3$ is equivalent to what base ten common fraction?
• How do you build a tank out of wood?
• How many bananas do you need to make enough radiation for a nuclear missile?
• How many bananas do you need in order to die of radiation?
• Can you do percents with binary?
• Did you guys know that $64$ is the smallest positive integer that is both a perfect square and perfect cube besides $1?$
• There is a ten-digit 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 $10.$ What is the number? (Variation: What if each digit was only used once?)
• Let $\bigtriangleup ABC$ be an equilateral triangle of length $3$ that has mirrors as sides. What is the shortest distance a light beam, starting from point $A,$ would have to travel to end at point $B?$ (From the 2015 Knights of Pi Math Tournament, run by the Newport Math Circle.)
• If you go to the movies and you're paying, is it cheaper to take one friend to the movies twice, or two friends to the movies at the same time?
• How do you push yourself to solve more problems? Of late, I've been acting a bit lazy, but I've realized that I can do more, but I'm unable to push myself to complete a problem in the stipulated time.

[RZ923]

The one with the ten digit number was my question I logged.
Sadly I couldn’t come today.

[debbie]

@RZ923 Yes, I replied to your other post in "Early Bird Question"! Sorry that you weren't there, but at least you can watch the replay!

[debbie]

Topics from the Wed 6/24/20

• Three points are chosen randomly and independently on a circle. What is the probability that all three pairwise distances between the points are less than the radius of the circle?
• I am an odd number. Take away a letter and I become even. What number am I?
• I add $5$ to $9$ to get to $2.$ This is correct, so how is this possible? (Answer: On a clock.)
• Is there any math in games such as Minecraft?
• Find three positive rational numbers $a, b,$ and $c$ such that $a + b + c = a \times b \times c = 7.$
• What three numbers, none of which is zero, give the same result no matter whether they're added or multiplied?
• At what points on Earth can you travel in a perfectly straight line and go due east at the same time?
• Can you arrange four $9$'s to make it equal to $100?$

[debbie]

Topics from the Friday 6/26/20 live stream

• If $f(0.25) = 0.5$ and $f(0.5) = 0.5,$ how can we find $f(x)?$ (Lagrange Interpolation)
• Po the cat is catching fish! He has a $\frac{1}{3}$ chance of catching a salmon, $\frac{1}{8}$ change of catching a trout, and $\frac{1}{10}$ chance of catching a hallibut. How much chance does he have of catching a shrimp?
• What is $x + x - x^{-2}$ if $x = 5?$
• How many people do we need to watch the stream for Ask Math Anything to continue?
• If $a + b = \frac{a}{b} + \frac{b}{a},$ find $a^2 + b^2.$
• What fractions are equivalent to $\frac{1}{2}?$ Can you list all of them?
• Suppose you have $3$ variables; is it possible to have only $2$ equations with a definite answer for all variables?
• What is a real number?
• How is it possible to have an irrational measurement?
• We know that in a right-angled triangle, $\text{hypotenuse}^2 = \text{base}^2 + \text{perpendicular}^2.$ What will be the relation if we cube them?

[debbie]

Topics from the Saturday 6/27/20 live stream

• What professions are fit for math majors?
• Are people who are blind better at hearing?
• Do you recommend looking at the MATHCOUNTS School Handbook every day?
• Can we talk or yell something in ultrasound?
• What types of things should we memorize?
• What do you teach at CMU?
• What is an undergraduate student?
• Who invented your theme song?
• Do you like China's education system, with lots of homework, memorization, and competition?

[debbie]

Topics from the Monday 6/29/20 live stream

• What is the easiest way to solve this question? "A printer users 300 digits to number the pages of a book. How many pages are in the book? (The book starts at Page 1.)

• The product of two prime numbers is 9 more than their sum. What is their absolute difference?

• What is the difference between $\pi$ and $\phi?$ (Relates to the golden ratio!)

• In a sequence the terms are $2, 6, 12, 72, \ldots$ where, starting with the 3rd term, every term is the product of the last two terms. If the $9^{\text{th}}$ term is $2^a * 3^b,$ what is $a + b?$

• What's the difference between the Po-Shen Loh ratio and the Daily Challenge ratio?

• If you had to eat one of these, which one would you eat? Crispy Apple, Savory Popcorn, or Sweet Energy Bar?

• How can you make the following equation true by drawing only one straight line? $5 + 5 + 5 = 550$

• If a truck goes at a speed of $2^x$ mph on the $x$th minute, then how many miles does it go in $1$ hour?

• Use eight $8$'s and the operations of addition, subtraction, multiplication, division, exponentiation, factorials and square roots to make $1000.$

• What is the max distance between two watchers of today's AMA (Ask Math Anything)?

[debbie]

Topics from the Tuesday 6/30/20 live stream

• The graph of $y = 3x^2 - 2x + k$ has an x-intercept of $2.$ What is the value of $k?$
• We wish to make a 3-Senator committee in which no two members are from the same state. How many ways can we choose three states to be represented?
• A duck was given $\$9,$ a spider was given $\$36,$ a bee was given $\$27.$ Based on this information, how much money would be given to a cat?
• How to lay out $51$ stars on the U.S. flag
• How does the vector dot product relate to the area of a paralellogram?
• What are the chances that your water will taste like bananas?
• How can you find all the dogs and cats in America using math?
• Move one number in $123 + 252 = 748$ in order to get a true math statement.
• Do you agree that mosquitoes should be wiped out of existence?
• Where have the old Daily Challenge videos gone?
• There's an $8$-digit number that is divisible by $1, 2, 3, 4, 5, 6, 7,$ and $8.$ The number is a perfect number and all the digits are different. What is this number?
• What if it literally rained cats and dogs?
• Let $P(x)$ be a polynomial with nonnegative integer coefficients. If $P(1)=5$ and $P(4) = 83,$ then what is $P(3)?$
• I am bad at math; what is the point of listening if I can't understand?
• If $66=2, 999=3, 8=2, 0=1, 9696=4, 8123=2, 98=3,$ and $88=4,$ what does $816982$ equal?
• My friends learned python already and I don't want to be the odd one out so I'm learning Python on the internet by myself. I don't go to any courses, so it's kind of hard. Any advice?

[RZ923]

@debbie said in Today's Topics (June 2020):

• There is a ten-digit 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 $10.$ What is the number? (Variation: What if each digit was only used once?)

This problem is mine.
I am watching the recordings now
37:06: “This is from Vera Weng...”
I didn’t even attend the livestream lol
(Also another huge thanks to @debbie for logging it in!)
(I was meant to say: all digits are unique, but I forgot to say this while logging it in)
PS I posted a comment below the livestream as Vera Weng.

[debbie]

@RZ923 Yes, I definitely know who you are by now. Same for many others Even still, I would like to protect people's privacy by not providing their usernames. It is so great to see you as well as many other familiar faces at the live streams!