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    Today's Topics (July 2020)

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    • debbieD
      debbie ADMIN M0★ M1 M5
      last edited by

      • I have a bag that has some green and yellow coins. A green coin is worth 5 bananas, and a yellow coin is worth 7 bananas. What is the largest number of bananas the bag cannot be worth? (The Chicken McNugget Theorem)

      • How do you find the square root of a missile launch speed? I need to know by Friday! --- A.

      • What is the least non-even non-prime factor of \(2019^8 + 1\) (This question was aborted after it was revealed to be an AIME #13 question.)

      • Let \(\bigtriangleup ABC\) be a right triangle with hypotenuse \(\overline{AC}.\) Suppose that \(AB = 5, AC = 10,\) and \(D\) is the point where the bisector of angle \(\angle A\) intersects \(\overline{BC}.\) What is the length of \(\overline{AD}?\) --- L.

      • Do you pour the milk first or the cereal first in your bowl?

      • A story about fires in British colleges with a very unique origin.... (Find out the rest in "Overheard"!)

      • Is matrix multiplication not always commutative? Why?

      • Is the responsibility of being a teacher sometimes overwhelming?

      • Suppose \(x\) is a perfect square greater than \(100,000\) and its digits are arranged in ascending order. What is \(x?\)

      • Have you ever had pasta with only shredded cheese?

      • What is \(123123\) divided by \(1001?\)

      • I have a broken calculator. I was doing homework on my desk and wanted a little more room for my arm. I shoved the calculator off. Broken. \(54 = 14, 67 = 19, 92 = 20.\) What is \(73?\)

      1 Reply Last reply Reply Quote 4
      • debbieD
        debbie ADMIN M0★ M1 M5
        last edited by

        Topics from the Thursday 7/2/20 live stream

        • What is the smallest possible sum of squares of 2 numbers, if their product is \(-16?\) (And the AM-GM (Arithmetic Mean - Geometric Mean Inequality))

        • Let \(x\) be a number less than \(100.\) If the square of \(x\) has its tens digit odd, what is the units digit of the square of \(x?\)

        • If you hit your face really hard, and it hurts really bad, are you strong or weak?

        • Can you please explain what an "argument" or "modulus" is?

        • Is your shirt made of bananas? (Prof. Loh wore a yellow shirt today!)

        • A triangle has sides \(x, x+4, \) and \(3x-5.\) What is the possible range of \(x?\)

        • If \(a \times b \times c = 10, a - b - c = 10, a > b,\) and \(b > c,\) then what is \(a, b,\) and \(c?\) (This was too messy to calculate...)

        • Po the dolphin is texting his friends Debbie and v4913 in class! When he uses messages, he has a 30% chance of being caught. The chance of getting caught while using Facebook is 40% and the chance of getting caught while using Instagram is 80%. What should he use in order to get a 50% chance of getting caught?

        • How is NOVID going?

        • What are the most important math classes for programming? I've heard discrete math and linear algebra are essential.

        • How to find passion for things

        • What's your favorite color? (Answer: the Expii / Daily Challenge bluerple)

        RZ923R 1 Reply Last reply Reply Quote 3
        • RZ923R
          RZ923 M0★ M2★ M3★ M4★ M5 @debbie
          last edited by RZ923

          @debbie
          E3DF8E6F-2FFD-49F8-AF62-65C83AF4BAC0.jpeg
          Banana shirt 🍌 👕

          Very Interesting

          1 Reply Last reply Reply Quote 2
          • debbieD
            debbie ADMIN M0★ M1 M5
            last edited by

            Topics from the Friday, 7/3/20 live stream

            • A man completes a trip in 10 hours. He travels half of the trip's distance at the rate of \( 21 \text{ } \frac{\text{km}}{\text{hr}} \) and the second half at the rate of \(24 \text{ } \frac{\text{km}}{\text{hr}}.\) Find the total distance of the trip in kilometers. (Harmonic mean time!)

            • How does a black hole defy physics?

            • I was doing my math homework while in the bathroom. I accidentally dropped my calculator in the toilet. Now, \(5 + 4 = 30, 8 + 6 = 64, 5 + 5 = 35, 9 + 1 = 27.\) What is \(9 + 3?\)

            • There are two numbers whose product added to the sum of their squares is \(109,\) and whose difference of squares is \(24.\) What are the two numbers?

            RZ923R The Blade DancerT 2 Replies Last reply Reply Quote 3
            • RZ923R
              RZ923 M0★ M2★ M3★ M4★ M5 @debbie
              last edited by

              @debbie We have so little topics today!

              Very Interesting

              debbieD 1 Reply Last reply Reply Quote 1
              • debbieD
                debbie ADMIN M0★ M1 M5 @RZ923
                last edited by

                @RZ923 Yes, lol, Prof. Loh was explaining each question for a long time! 🙂

                1 Reply Last reply Reply Quote 3
                • The Blade DancerT
                  The Blade Dancer M0★ M1★ M2★ M3★ M4 M5 @debbie
                  last edited by

                  @debbie I hereby decree that one shall never complete their home assignments whilst in the lavatory.

                  The Blade Dancer
                  League of Legends, Valorant: Harlem Charades (#NA1)
                  Discord: Change nickname if gay#7585

                  debbieD RZ923R 2 Replies Last reply Reply Quote 4
                  • debbieD
                    debbie ADMIN M0★ M1 M5 @The Blade Dancer
                    last edited by debbie

                    @The-Rogue-Blade I've forked this off to another thread, as it was drifting away from the topic 👍

                    1 Reply Last reply Reply Quote 1
                    • debbieD
                      debbie ADMIN M0★ M1 M5
                      last edited by debbie

                      Topics from the Saturday 7/4/20 live stream

                      • What curriculum do you recommend for kids to learn math like Algebra, etc.?

                      • Why is the area of a triangle related to base times height?

                      • How can I prepare for the USAMO if I already passed AMC and AOIME? What are the best resources?

                      • Why are graphing calculators so expensive?!?! (Tip from Prof. Loh: Buy the TI-85, since there is less demand for them, so they're cheaper!)

                      • I'm in elementary school and I know quadratic equations (3rd grade). Do you think I will get to Calculus in 6th grade?

                      • How do you win at cards? (Example: The game "War")

                      • What green screen, PC, streaming software, webcam and mic do you use?

                      • I always believe that one needs to do one thing regularly in order to keep your mind sharp. Is this true for Math? And how to make yourself not lose interest in things.

                      • When should one start learning Calculus?

                      • What would you eat if you were allergic to bananas? (Answer: Banana chilies 🌶 )

                      • Do you believe video games are healthy or not?

                      • Do you like moving? 🏃 🚴 🏋 🤹

                      • Will you be watching fireworks later today?

                      • Have you ever moved into a new house with your family?

                      • Why there should be math commentators for math events, similar to how there are sports commentators for sports events 🎤 🎵

                      RZ923R 1 Reply Last reply Reply Quote 2
                      • RZ923R
                        RZ923 M0★ M2★ M3★ M4★ M5 @debbie
                        last edited by

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

                        • Do you like moving? 🏃 🚴 🏋 🤹

                        🏃 🏊 🎾 🏓 🏋 🚴 🤹 🎱 🏸 ⚾ 🏀 🏹 🎳 🥊 🏏 🎯 🤺 🏑 🎣 🏈 🥅 🏌 🤾 🤸 ⛹ 🏒 🏇 🚵 ⛷ 🎿 🤽 🤼 🏄 🏉 🥋

                        (PS I hope this doesn’t count as spam)

                        Very Interesting

                        1 Reply Last reply Reply Quote 2
                        • RZ923R
                          RZ923 M0★ M2★ M3★ M4★ M5 @The Blade Dancer
                          last edited by

                          @The-Rogue-Blade lol 😂

                          Very Interesting

                          1 Reply Last reply Reply Quote 1
                          • debbieD
                            debbie ADMIN M0★ M1 M5
                            last edited by 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?

                            RZ923R 2 Replies Last reply Reply Quote 2
                            • RZ923R
                              RZ923 M0★ M2★ M3★ M4★ M5 @debbie
                              last edited by

                              @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

                              debbieD 1 Reply Last reply Reply Quote 2
                              • RZ923R
                                RZ923 M0★ M2★ M3★ M4★ M5 @debbie
                                last edited by

                                @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 🙂

                                Very Interesting

                                1 Reply Last reply Reply Quote 2
                                • debbieD
                                  debbie ADMIN M0★ M1 M5 @RZ923
                                  last edited by

                                  @RZ923 Yes! 🙂

                                  1 Reply Last reply Reply Quote 2
                                  • debbieD
                                    debbie ADMIN M0★ M1 M5
                                    last edited by

                                    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)

                                    1 Reply Last reply Reply Quote 2
                                    • RZ923R
                                      RZ923 M0★ M2★ M3★ M4★ M5
                                      last edited by

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

                                      Very Interesting

                                      debbieD 1 Reply Last reply Reply Quote 2
                                      • debbieD
                                        debbie ADMIN M0★ M1 M5 @RZ923
                                        last edited by

                                        @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. 🙂

                                        1 Reply Last reply Reply Quote 2
                                        • debbieD
                                          debbie ADMIN M0★ M1 M5
                                          last edited by

                                          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?

                                          1 Reply Last reply Reply Quote 2
                                          • debbieD
                                            debbie ADMIN M0★ M1 M5
                                            last edited by 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?

                                            RZ923R 1 Reply Last reply Reply Quote 2

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