Today's Topics (July 2020)

debbie

Topics from the Monday 7/6/20 live stream

There is a game. A guy draws 10 cards. There are 21 cards. There are 3 distinct cards: 1, 2, 3. There is an equal chance of being drawn. Find the chance that the other guy gets the sum of the cards drawn. (Not solved, but discussed. )
\(9_x + 10_x = 21_y\): "Nine in base \(x\) plus \(10\) in base \(x\) equals 21 in base \(y.\) What is \(x + y?\) There are multiple answers."
There is a number composed of \(94\) nines. There is also a number composed of \(95\) sevens. When you multiply these two numbers, what is the digit sum?
In how many ways can you arrange \(16\) bananas, \(17\) broken calculators and \(18\) Po-Shen Loh's?
Do you know any math competitions that allow calculators? (MATHCOUNTS! And talking about the super-spiffy TI-92 calculator.)
Find the next number in this sequence of numbers: \((325, 263, 642, 436, 374, 753, 547, 485, ? )\)
When you wrote your name in school, did you write the hyphen too? (Answer: Yes, because Prof. Loh's brother and sister were also named "Po." )
How many ways can a person go from \((0,0)\) to \((m,m)\) without touching the diagonal? (Not solved, since this is a famous problem having to do with Catalan Numbers.)
Write the biggest number you can with nine \(9\)'s. (No factorials allowed)
Can I have your contact for math assistance? I'm very curious but lacking help.
If \( \mid x - 1 \mid \mid 2x - 4 \mid = 5,\) then what is the range of \(x?\) (This turns into a quadratic!)
How can you prove the Pythagorean Theorem? (Answer: Go to the free daily.poshenloh.com lesson in Module 0, Day 1)
A calculator can display ten digits. How many different ten-digit numbers can I type using just the 0-9 keys once each, and move from one keypress to the next using the knight move in chess? (This was a famous riddle called, "Knight's Tour.")
Which types of problems do you choose to solve in this stream?

RZ923

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

\(9_x + 10_x = 21_y\): "Nine in base \(x\) plus \(10\) in base \(x\) equals 21 in base \(y.\) What is \(x + y?\) There are multiple answers.

Did you mean infinitely many solutions?

RZ923

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

When you wrote your name in school, did you write the hyphen too? (Answer: Yes, because Prof. Loh's brother and sister were also named "Po." )

Po-Ru Loh and Po-Ling Loh

debbie

@RZ923 Yes!

debbie

Topics from the Wednesday, 7/8/20 live stream

How can you roll a dice and always get 6?
If everyone in the world turned all their lights in their home on at the same, what would happen?
Does a human being spend more energy than a vacuum cleaner?
How come I can't come up with a good question to ask?
An Olympic cyclist can only produce enough watts (about 800) to power a toaster.
Find \( 3(m^2)(n^2)\) if \(m^2 + 3(m^2)(n^2) = 30n^2 + 517.\)
Who came up with the idea that rabbits eat carrots?
How do we know if a cubic equation has real or imaginary roots? (And brief mention of Descartes' Rule of Signs)
How to improve in math from having a no-math background?
Find all ordered pairs \((x,y)\) of real numbers such that \(3^{x^2-2xy} = 1\) and \(x^2 = y + 3.\)
Find a 5-digit perfect square with the property that its digits can be arranged to form another 5-digit perfect square.
Po-Shen Loh is captured by me in a room with no air vents. The air runs out in 5 minutes. If Po-Shen Loh faints from lack of air, he is let out of the room. Is there a way to survive without escaping?
Show that if some integer \(n\) divides a Fibonacci number, then it will divide infinitely many Fibonacci numbers (Didn't actually solve this, but discussed it briefly.)
Why were you so late today? (Answer: was talking to colleges about them using NOVID for their students)

RZ923

@debbie Sorry if this sounds rude, but can you please update the Fri 10 July livestream topics and overheard?
Thanks

debbie

@RZ923 It's not rude; thanks for the reminder! I was swamped with a lot of things yesterday, but I'll make sure to post the Overheard and Today's Topics very soon today.

debbie

Topics from the Friday 7/10/20 live stream

How many subsets of \( (1, 2, 3, 4, \ldots, 12\) have exactly 1 or 2 primes?
When \(x^2 - 5x + 3c\) is divided by \(x-3,\) the remainder is \(12.\) What is the value of \(c?\)
One-inch squares are cut from the corners of a \(5\)-inch square. What is the area in square inches of the largest square that can fit into the remaining space?
In rectangle \(ABCD,\) we have \(A = (6, -22), B = (2006, 178), D = (8, y),\) for some integer \(y.\) What is the area of the rectangle \(ABCD?\)
Is there a quick way to solve the problem where two cars are coming towards each other and a fly is flying in between? How much distance does the fly travel when the cars collide?
If you have done 20 questions on the AMC 10, and you have 5 questions you don't know how to do, how many questions should you guess on to have the highest expected score?

debbie

Topics from the Friday, 7/17/20 live stream

How many zeroes are at the end of \(126! - 125!?\) (That's 126 factorial )
Why are quadratics called quadratics?
\(ABC\) is a triangle. Let \(D\) be the midpoint of \(\overline{BC},\) \(E\) is a point on \(\overline{AC},\) \(\overline{AB}\) and \(\overline{DE}\) are parallel. \(\overline{AD}\) and \(\overline{BE}\) intersect at point \(F.\) If \(AEF\) has an area of \(1,\) what is \(ABC?\)
How do you factor quadratics using the quadratic formula?
If \(AB\) in base \(7\) is equal to \(BA\) in base \(9,\) what is the number in base \(10?\)
Turn me on my side, and I am everything. Cut me in half, and I am nothing. What am I? (Answer: \(8\) )
Is it possible for a line to contain irrational points? (Yes, if it's vertical or horizontal.) What if we want a line that has slope not \(0\) or infinite or undefined? (Answer: irrational slope and intercept will do the trick!)
Which countries share the longest international border? (Answer: U.S. and Canada )
How many four-digit numbers with two middle digits of \(7\) or \(9\) (not necessarily in that order) are divisible by \(45?\)
Find all the possible values for \(ln{ (e^x)}.\)
Can you give an example of an undefinable real number?
I am a famous mathematician. If you change a letter in my last name, you might be able to measure how tall you are. Who am I? (Answer: Euler)
Minecraft Po goes mining for diamonds! He finds \(21\) cobblestones, \(1\) diamond, and \(108945\) coal! What percent of the stuff he found is cobblestone?
Which field of mathematics will grow the most in coming times?
Is there trigonometry for shapes with more angles than three?
How long are you going to do live streams?
How is MOP going?
Are there any conditions to be on the math team that you run?

RZ923

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

Turn me on my side, and I am everything. Cut me in half, and I am nothing. What am I? (Answer: \(\infty\) )

Shouldn’t the answer be \(8\)?

debbie

@RZ923 Yes, you're right; thanks!

The Blade Dancer

Shouldn't that be 8 because then it becomes infinite

Also Debbie's to do list be like: https://www.youtube.com/watch?v=zGl796352RI

debbie

@The-Rogue-Blade Sorry, I missed that... what did you say again? I was looking at my list of things to do...

debbie

Topics from the Friday 7/24/20 live stream

The mean of a list of \(12\) numbers is \(13,\) and the modes are \(a, b, c, d.\) If \(a + 2, b - 6, c + 1,\) and \(d - 3\) are distinct numbers in this list, and none of them are modes of the list, then what is \(a + b + c + d?\)
In triangle \(\bigtriangleup ABC, AB = 13, BC = 14, CA = 15\) and \(M\) is the midpoint of \(\overline{BC}.\) Let \(P\) be a point on the segment \(AM\) so that \(\angle BPC + \angle BAC = 180^{\circ}.\) Find \(MP \times MA.\)
Three fair six-sided dice are rolled. What is the probability that the values shown on two of the dice sum to the value shown on the remaining dice?
Which do you think is more important for kids learning math: more depth (digging deeper into only a few topics), or more width (learning more topics, but only learning a bit of each?)
Po the dolphin answers my question. He answers \(500\%.\) What is the chance that he will answer this problem with \(500\%\) again?
How to multiply two or more numbers in less than \(15\) seconds without using a calculator.
I was dumpster diving when I found a broken calculator. \(4 = 1, 3 = 3, 5 = 0, \) and \(6=?\)
Suppose you are at a distance of \(r\) above a planet of radius \(r.\) How much of the planet is visible?
How many ways are there to choose \(5\) books from \(12\) books with no neighboring books chosen?

debbie

Topics from the Friday 7/31/20 live stream

How many zeroes are there from all the integers from \(1\) to \(25\) in binary?
Let \(S\) be the set of points determined by \( \left| |x|-2 \right| + \left| |y|-1 \right| = 1.\) If a model of \(S\) were built from wire of negligible thickness, then what is the total length of wire required?
\(G\) is an \(8 \times 8\) grid with a \(1\) written in each of its unit squares. An operation consists of multiplying all entries in a row or column by \(-1.\) How many distinct grids can be obtained by applying this operation to \(G\) a finite number of times?
Is it possible that geometry can be proved by algebra?
What is your chess rating?
How hard it is to get into Carnegie Mellon University?
What majors does Carnegie Mellon specialize in?
Can you get your channel certified? Like get that check mark next to your channel name?