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    Today's Topics (June 2020)

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    • debbieD
      debbie ADMIN M0★ M1 M5
      last edited by debbie

      Topics from the Friday 6/19/20 live stream

      • Please explain the metallic ratios (gold, silver, etc.)
      • Is the myth true that the golden ratio appears in the Mona Lisa?
      • Didn't Da Vinci invent the Ornithopeter or whatever it's called? (Helicopter-like flying machine.)
      • One fourth of the population of a newly discovered planet have 4 legs. The rest have two legs. There are 60 legs total. How big is the population of the newly discovered planet?
      • If \( a + b + c = 10, a \times b \times c = 30,\) what is the value of \(a^2 \times b^2 \times c^2?\) (Many possible solutions.)
      • Prove that if you square root any positive number (it doesn't have to be an integer, and it can't be 0,) an infinite number of times, you will get 1.
      • There is a toilet roll whose radius is \(4\) and the "empty part" of the roll has a radius of \(1.\) What is the length of the paper if we unroll the toilet paper? (Audience contributed helpful numbers: 375 sheets per roll in Singapore, 276 layers in one roll (counted by hand), 0.0004 inches per sheet)
      • How many bananas do you eat every day? (Answer: 1)
      • Do you use bootstrap for your websites?
      • How do you build a thermonuclear missile with a launch site using only metal and 10 pounds of plutonium? I need to know by Friday because that's when my geometry is due.
      • Why do you love math?
      RZ923R 1 Reply Last reply Reply Quote 2
      • RZ923R
        RZ923 M0★ M2★ M3★ M4★ M5 @debbie
        last edited by RZ923

        @debbie
        I was sorry I couldn’t attend today’s livestream.
        For the question where:
        \(a+b+c=10\)
        \(a\times b\times c=30\)
        \(a^2\times b^2\times c^2=?\)
        I don’t get why you put “unsolvable”.
        Shouldn’t it be:
        \(a=2,b=3, c=5\)(or some other way around)
        \(a^2\times b^2\times c^2=4\times 9\times 25=900\)?

        Very Interesting

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

          @RZ923 Thanks for your comment! I actually meant that there are many solutions. The set of equations doesn't uniquely determine a single solution. So "unsolvable" isn't exactly the right word. For example, another solution is \(a = \sqrt{3}i, b = -\sqrt{3}i, c = 10.\) Then we would have

          $$ a + b + c = \sqrt{3}i - \sqrt{3}i + 10 = \boxed{10} $$
          $$ a \times b \times c = \sqrt{3}i \times -\sqrt{3}i \times 10 = 3 \times 10 = \boxed{30} $$

          Thanks for pointing this out. 🙂

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

            Newport Math Club Knights of Pi Math Tournament Special Livestream Saturday 6/20/20

             

            Questions from Newport Math Club:

            • Find the sum of the digits of the sum \( 9 + 99 + 999 + 9999 + … + 999999999 \) (nine 9’s)

            • Marisa draws a five-point star by extending the sides of a convex pentagon with all angles less than 120°. What is the sum of the angles of the points of her star, in degrees?

            • How many solutions does the equation \(2^x = x^2 \) have for some real value of \(x?\)

            • If everyone is connected to all the people they’ve ever greeted, how many degrees of separation is the world away?

            • If we met an alien civilization and exchanged mathematics, what maths do you think would be similar, and what would be different? Would they have things like real numbers?

            • What does convex mean?

            • Compare CMU and Caltech

            • Can you describe your stack from Caltech's Ditch Day?

            • Would you rather win the Nobel Prize or "invent" math?

            • How can you predict when a popsicle will melt?

            • How does base \(\frac{1}{37}\) work?

            • Would you rather have cake, ice cream, or cupcakes for the rest of your life?

            • Have you ever participated in an Improv Troupe? If so, how was your experience?

            • If a jet goes 90 mph, and a monkey goes 5 mph, and if the monkey drops from a tree it goes 4 miles per hour. How fast does a banana go if the monkey jumps for 5 hours?

            • What would happen if someone used a sonic boom on NOVID? (Relates to this BBC documentary about pistol shrimps)
               
              temp-pistol-shrimp.png
               

            • How do I make a nuclear reactor?

            • Can you give some advice on trading? (And some mention of how oil prices went negative in April...)

            • How do I infiltrate the ISS (International Space Station)?

            • Metric or Imperial system for measurements? (foot, inch, barley grain = smallest unit of weight in the troy and avoirdupois systems, equal to \(\frac{1}{5760}\) of a pound troy, and \(\frac{1}{7000}\) of a pound avoirdupois (approximately 0.0648 grams)

            • Besides math and programming, do you have other hobbies that you do in your free time?

            • Can someone hack NOVID?

            divinedolphinD 1 Reply Last reply Reply Quote 3
            • divinedolphinD
              divinedolphin M0★ M1★ M2★ M3★ M4★ M5★ M6★ @debbie
              last edited by divinedolphin

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

              • How do I infiltrate the ISS (International Space Station)?

              haha

              👕👕👕👕👕👕👕👕👕👕🍌🍌🍌🍌🍌🍌🍌🍌🍌🍌

              sqwishyS 1 Reply Last reply Reply Quote 2
              • sqwishyS
                sqwishy M2 M3 M4★ @divinedolphin
                last edited by

                @divinedolphin haha 🤣

                1 Reply Last reply Reply Quote 2
                • The Blade DancerT
                  The Blade Dancer M0★ M1★ M2★ M3★ M4 M5
                  last edited by

                  Ooh can I go when you do infiltrate it

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

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

                    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 \(1800 \text{ } \text{m}^3?\)
                    1 Reply Last reply Reply Quote 1
                    • debbieD
                      debbie ADMIN M0★ M1 M5
                      last edited by

                      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?

                      1 Reply Last reply Reply Quote 1
                      • debbieD
                        debbie ADMIN M0★ M1 M5
                        last edited by 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.
                        RZ923R 1 Reply Last reply Reply Quote 1
                        • RZ923R
                          RZ923 M0★ M2★ M3★ M4★ M5
                          last edited by

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

                          Very Interesting

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

                            @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!

                            1 Reply Last reply Reply Quote 1
                            • debbieD
                              debbie ADMIN M0★ M1 M5
                              last edited by 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 \(100?\)
                              1 Reply Last reply Reply Quote 1
                              • debbieD
                                debbie ADMIN M0★ M1 M5
                                last edited by

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

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

                                    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)?

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

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

                                        Very Interesting

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

                                          @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!

                                          1 Reply Last reply Reply Quote 1

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