Today's Topics (July 2020)
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@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?
Very Interesting
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@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."
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Po-Ru Loh and Po-Ling Loh
- 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."
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@RZ923 Yes!
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Topics from the Wednesday, 7/8/20 live stream
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How can you roll a dice and always get 6?
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If everyone in the world turned all their lights in their home on at the same, what would happen?
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Does a human being spend more energy than a vacuum cleaner?
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How come I can't come up with a good question to ask?
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An Olympic cyclist can only produce enough watts (about 800) to power a toaster.
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Find \( 3(m^2)(n^2)\) if \(m^2 + 3(m^2)(n^2) = 30n^2 + 517.\)
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Who came up with the idea that rabbits eat carrots?
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How do we know if a cubic equation has real or imaginary roots? (And brief mention of Descartes' Rule of Signs)
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How to improve in math from having a no-math background?
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Find all ordered pairs \((x,y)\) of real numbers such that \(3^{x^2-2xy} = 1\) and \(x^2 = y + 3.\)
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Find a 5-digit perfect square with the property that its digits can be arranged to form another 5-digit perfect square.
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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?
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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.)
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Why were you so late today? (Answer: was talking to colleges about them using NOVID for their students)
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@debbie Sorry if this sounds rude, but can you please update the Fri 10 July livestream topics and overheard?
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@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.
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Topics from the Friday 7/10/20 live stream
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How many subsets of \( (1, 2, 3, 4, \ldots, 12\) have exactly 1 or 2 primes?
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When \(x^2 - 5x + 3c\) is divided by \(x-3,\) the remainder is \(12.\) What is the value of \(c?\)
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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?
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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 \(ABCD?\)
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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?
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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?
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Topics from the Friday, 7/17/20 live stream
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How many zeroes are at the end of \(126! - 125!?\) (That's 126 factorial
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Why are quadratics called quadratics?
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\(ABC\) 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 \(ABC?\)
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How do you factor quadratics using the quadratic formula?
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If \(AB\) in base \(7\) is equal to \(BA\) in base \(9,\) what is the number in base \(10?\)
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Turn me on my side, and I am everything. Cut me in half, and I am nothing. What am I? (Answer: \(8\)
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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!)
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Which countries share the longest international border? (Answer: U.S. and Canada
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How many four-digit numbers with two middle digits of \(7\) or \(9\) (not necessarily in that order) are divisible by \(45?\)
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Find all the possible values for \(ln{ (e^x)}.\)
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Can you give an example of an undefinable real number?
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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)
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Minecraft Po goes mining for diamonds! He finds \(21\) cobblestones, \(1\) diamond, and \(108945\) coal! What percent of the stuff he found is cobblestone?
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Which field of mathematics will grow the most in coming times?
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Is there trigonometry for shapes with more angles than three?
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How long are you going to do live streams?
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How is MOP going?
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Are there any conditions to be on the math team that you run?
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@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 \(8\)?
- Turn me on my side, and I am everything. Cut me in half, and I am nothing. What am I? (Answer: \(\infty\)
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@RZ923 Yes, you're right; thanks!
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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
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@The-Rogue-Blade Sorry, I missed that... what did you say again? I was looking at my list of things to do...
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Topics from the Friday 7/24/20 live stream
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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 \(a + b + c + d?\)
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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 \(MP \times MA.\)
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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?
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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?)
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Po the dolphin answers my question. He answers \(500\%.\) What is the chance that he will answer this problem with \(500\%\) again?
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How to multiply two or more numbers in less than \(15\) seconds without using a calculator.
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I was dumpster diving when I found a broken calculator. \(4 = 1, 3 = 3, 5 = 0, \) and \(6=?\)
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Suppose you are at a distance of \(r\) above a planet of radius \(r.\) How much of the planet is visible?
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How many ways are there to choose \(5\) books from \(12\) books with no neighboring books chosen?
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Topics from the Friday 7/31/20 live stream
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How many zeroes are there from all the integers from \(1\) to \(25\) in binary?
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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?
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\(G\) 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?
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Is it possible that geometry can be proved by algebra?
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What is your chess rating?
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How hard it is to get into Carnegie Mellon University?
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What majors does Carnegie Mellon specialize in?
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Can you get your channel certified? Like get that check mark next to your channel name?
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