Today's Topics (June 2020)
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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.
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The one with the ten digit number was my question I logged.
Sadly I couldn’t come today.
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@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!
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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 \(100?\)
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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?
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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?
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Topics from the Monday 6/29/20 live stream
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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.)
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The product of two prime numbers is 9 more than their sum. What is their absolute difference?
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What is the difference between \( \pi \) and \( \phi?\) (Relates to the golden ratio!)
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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 \(a + b?\)
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What's the difference between the Po-Shen Loh ratio and the Daily Challenge ratio?
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If you had to eat one of these, which one would you eat? Crispy Apple, Savory Popcorn, or Sweet Energy Bar?
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How can you make the following equation true by drawing only one straight line? \( 5 + 5 + 5 = 550\)
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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?
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Use eight \(8\)'s and the operations of addition, subtraction, multiplication, division, exponentiation, factorials and square roots to make \(1000.\)
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What is the max distance between two watchers of today's AMA (Ask Math Anything)?
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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?
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@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. -
@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!
