2018 Raytheon MATHCOUNTS National Competition hosted by Wil Wheaton

one of these remarkable young humans will become the 2018 national champion and the recipient of the 20 000 donald g weinert college scholarship important technical details follow the countdown round competition is a single elimination bracket tournament where the top four seeds will have a buy in the first round i will read a question while it is being projected on the monitor in front of the students and also on the large screen for the audience it is extraordinarily unlikely and by that i mean very likely that i will misspeak when reading a problem should that happen the problem showing on the students monitors and the audience screen will be considered the official problem students will have 45 seconds to solve the problem after it appears on the monitor there will be a green 45 second timer bar visible at the top of the screen the timer bar will change to yellow when there are 10 seconds remaining on the clock competitors once you have solved the problem press your buzzer i will call on the first person who presses the buzzer to announce his or her answer this is important do not announce your answer until i have called on you if you answer without buzzing your answer will not be recognized until you buzz in once i call on you you will have three seconds to complete your answer your opponent may continue working while you are answering the question if you answer incorrectly your opponent will have the remainder of the 45 seconds to buzz in and answer the question whoever answers the most out of five questions correctly and that is not necessarily three out of five will win the round and progress to the next round should the score be tied after five questions we will begin the sudden victory procedure this is exactly like sudden death with a less violent name this means that the next student to answer a question correctly in the matchup will win the matchup i'd like to wish you all good luck and let's get started with our first round match-up our eighth seed is samuel wang from virginia and our ninth seat is easton singer from ohio please come up and take a seat [Applause] welcome gentlemen uh samuel i have some information about you in front of me uh which i can see makes you uh uncomfortable excellent uh i understand that you're a huge harry potter fan is that correct uh yeah if you had to choose books or movies uh books uh and do you have a patronus uh no have you been officially sorted by pottermore uh yeah are you a ravenclaw no who are you slicing uh slytherin that would explain why i've never seen you in the ravenclaw library um well welcome and good luck easton you come to us from ohio uh and we asked our competitors if they could travel back in time where would they go and why and you said the 1980s so that you could observe the evolution of video game technology which i think is amazing uh do you have a favorite video game from the 80s uh we'll just go with pac-man yeah how do you feel about the sequels to pac-man ms pac-man junior pac-man pac-plus no just original pac-man yeah let me tell you you're very lucky you didn't live through the atari 2600 version of pac-man uh all right let's test out your buzzers easton go ahead and give your buzzer a try well it's lighting up but it's not making a sound that's going to be a problem uh while our technical gnomes work on solving that let's test samuel's buzzer go ahead samuel again there's no sound well i'm just going to look at the table in abject terror and figure out exactly how we fix this [Applause] oh there's some sounds coming while we wait for this to be repaired i forgot to tell you that samuel is in seventh grade from basis independent in mclean virginia and easton is in eighth grade from solon middle school in solon ohio all right let's give this another try easton yes samuel all right i have to say that was a little anticlimactic for me i thought the buzzer working would be more exciting all right are you ready all right the first question in round one comes now the question is what is the remainder when 2018 to the 2018 is divided by 20. samuel four the answer is four that is correct [Applause] that is one for samuel zero for easton let's move on to question number two and the question is in the figure equilateral triangle pqr is inscribed in isosceles triangle abc such that vertex r is the midpoint of side bc if the measure of angle bac is 28 degrees what is the degree measure of yes samuel 44. 44 degrees is correct [Applause] that gives samuel two i had a major star trek flashback reading that question question number three is up and the question is the hawks heat and hornets all played each other four times during the nba season the celtics played each yes samuel uh 20 to what 21 i'm sorry that is incorrect the celtics played each of those three teams twice how many total games were played yes easton 18. 18 games is the correct answer that is one point for easton two points for samuel we move on to question number four question number four is what whole number n makes six yes samuel thirteen uh that is incorrect six seventy is less than one over n is less than five fifty-sixths true yes easton twelve the correct answer is twelve and we are tied all right we are now to the final question in the round and the question is a standard grocery pallet measures 40 inches by 48 inches a case of cookies measures nine and a half inches wide by 14 and a half inches long what is the maximum number of yes easton 16. 16 is incorrect what is the maximum number of cases that can be placed directly onto the surface and within the boundaries of the palette 10 seconds samuel 12 12 is incorrect the correct answer is 13 cases this moves us on to not sudden death but in fact sudden victory all right gentlemen here is your question the question is if two x equals two and x minus yes samuel negative two negative two is incorrect if two x equals two and x minus y equals negative four yes easton the correct answer is six congratulations to both competitors congratulations to easton and moves on to the next round [Applause] this brings us to round two round two's competitors are as follows our fifth seed from puerto rico jessica wan and our 12th seed from michigan regan choi [Applause] welcome welcome it's nice to see you jessica you are in the sixth grade uh you attend saint john's school in san juan puerto rico and i understand that you like dogs yeah i also like dogs i'll tell you the truth i don't trust a person who doesn't like dogs uh what is your favorite breed of dog um pomeranians and do you have a pomeranian dog if you could have any dog in the world real or fictional pick a dog excellent that's what i figured you would say uh welcome and good luck and regan you come to us from michigan you're in the eighth grade you attend buland park medical school in troy michigan uh and i understand that you like to eat extremely spicy foods uh you sound like a danger seeker uh tell us what is one of the hottest things you've ever eaten uh there's this type of noodle in korea it's like like really spicy it's yeah yeah and you've eaten an entire bowl of these noodles yeah you are a madman and i love it uh let's give your buzzers a try we can go ahead and give your buzzer a try excellent and jessica all right everything seems to be in working order let us begin round two here is question number one good luck to both of you what is the closest integer to the value of the expression the quantity 2018 times the square root of 2018 minus 1 all over the quantity 2018 plus the square root of 2018 plus one jessica 44 the correct answer is 44. that brings jessica on the board with one point question number two the question is charlotte places a coin on the center square marked m in the seven by seven grid shown how many ways are there for her to spell math by moving to three other squares if for each move she can move the coin to either a square with a common side or a diagonally adjacent square jessica 72 i'm sorry that is incorrect 10 seconds regan 144 i'm sorry that is incorrect the correct answer is 104 ways all right the score is unchanged and it is time for question number three and the question is what is the slope of a line perpendicular to the hypotenuse of a triangle with vertices x negative one negative one y two negative one and z negative one three express your answer as a common fraction yes three over four three over four is correct that ties our score at one it is time for question number four and the question is there are two integer values of n that yield an integer value for the quantity 12 minus the square root of n all over the quantity four minus the square root of seven what is the sum of these two values of n 10 seconds regan 107 that is incorrect and time has expired the correct answer is 207. that's a guess extraordinarily controversial moment here in the countdown round all right the score is still tied at one as we move on to our next question and the question is if 3289 times 10 912 minus 299 times 992 equals 299 times 992 times k what is the value of k uh jessica 120 120 is correct that is the end of the round jessica juan you will advance regan thank you very much for competing [Applause] i'm not even answering these questions and i'm sweating our next mathletes come to us from florida it is jaden white as our sixth seed and our 11th seed comes from california william chen please take a seat welcome [Applause] jadon i understand that you enjoy counting the number of steps when you climb stairs yes uh how do you handle an escalator i don't i don't like cutting a number of steps in escalators yeah i'm not a big fan either have you ever been stuck on an escalator when they break down no i was trapped on one for hours it's terrifying do you mean an elevator oh no i mean an escalator william chen from the great state of california um i understand that you want to be an international math olympiad coach is that true yes that is amazing um we actually have a math counts alum here today who is a current imo coach that's pochen lo pochen are you in the audience you want to stand up and make some noise [Applause] now listen not to go all important to being earnest on you guys but maybe when this is over you can meet and discuss what it takes to be a math olympiad coach all right gentlemen are you ready let's test your buzzers william or jadon that also works i like your initiative william that's great oh and i forgot again jaydon you come to us uh you're in the eighth grade uh william i don't know what grade you're in because the truth is i don't know this it was just written on the monitor and i'm very embarrassed uh and it is now time to begin the round good luck to both of you here is question number one jim genie and their five children live in a 700 square foot apartment they want to move to a house for which the ratio of square feet to children is triple the apartment's ratio of square feet yes william 2 100. i'm sorry that is incorrect they want to move to a house for which the ratio of square feet to children is triple the apartment's ratio of square feet to total people how many square feet should their new house be jadon 2940 i'm sorry that is incorrect the correct answer is 1 500 square feet but in a way you're right you shouldn't cram a family of seven into 1500 square feet uh no score on the board let's move on to question number two the four largest numbers in a set of seven numbers have a mean of ten the four smallest numbers in the same set have a mean of five what is the least possible sum of the seven numbers yes william 50. the correct answer is 50 and william is on the board [Applause] it is time for question three and the question is if x circle r equals x squared plus r and p triangle h equals p over h plus p yes william 25 i'm sorry that is incorrect what is the value of 3 circle 7 quantity triangle 4 quantity triangle 5. 24 is correct and we are tied [Applause] here is question number four and the question is in isosceles trapezoid abcd sides a b and dc are parallel and the measure of angle adc equals the measure of angle bcd equals 88 degrees yes jadon 45 that is incorrect aubrey reflects this trapezoid across each of its non-parallel sides to produce two new trapezoids as shown by continuing to reflect each new trapezoid across its short side she creates a ring in which every trapezoid is adjacent to two other ones how many trapezoids are in the ring when it is completed 10 seconds yes william 90. the correct answer is 90. [Applause] question five is up william you have two jadon you have one and the question is what is the greatest prime factor of 2 to the 13th plus 2 to the 11th minus 10. 31 the correct answer is 31 and we are tied [Applause] all right are you both ready all right here we go the sudden victory question is the 10 centimeter measuring stick shown has marks at 2-5 there is a glitch i'm sorry one moment stand by my card stuck together we call that pulling a wheaton i apologize how would we like to handle this card number 17. the next good one is card number 18. we'll go to number 19. uh my deepest apologies i blame friction oh no let's go to 20. all right so now we're ready guys oh well are we ready for question 19. all right the question is if n equals 24 plus 30 plus 36 plus 42 plus 48 yes william 13. the correct answer is 13. great job both of you william chen answers to the next round [Applause] this brings us to round four of the countdown round please welcome the seventh seed alan chen from pennsylvania and from california the 10th seed mr jack albright [Applause] hello welcome uh jack you are in eighth grade and you attend the nueva school in los altos california one of the survey questions we asked was which superpower would you like to have and you and i could probably talk about that for the rest of the day you said having the ability to stop time would make you more powerful than one of the greatest characters from all of fiction who is this character and i forgot i forgot why i foot down yeah but it's careful from safe by the bell and pretty much so you can go like you can like time out and right that would be zack morris yeah zach who was good at the timeout yeah i mean stopping time for like up to a minute and two minutes that's already really really strong how would you handle the issue of you over time aging considerably more slowly than all of your peers they would begin to notice makeup that is an excellent answer that's actually how we do it in hollywood okay alan you are in eighth grade you attend ingomar middle school in sewickley pennsylvania and you told us that one of your favorite shows is master chef because you like eating good food uh is there a particular food that you have always wanted to try that you've never had the opportunity to try um not really like just you walk in and you're just like none of this impresses me i've had it all but that's amazing do you have a particular favorite masterchef competitor um now yeah i'm not a always do-wise excellent uh all right it is time for round four uh gentlemen let's test your buzzers alan give your buzzer a girl jack you are uh for the purposes of that question alan okay very good [Laughter] all right are we ready all right let's go the question is frank bounces a rubber ball from a height of 80 inches each time the ball bounces it bounces to a height of 75 percent of the height of the previous bounce how many bounces will the ball take before it first bounces to a height of less than 10 inches alan seven is incorrect [Music] six six is incorrect the correct answer is eight bounces you were both very close question number two the question is in square units what is the area of the triangle with vertices p negative two one q 3 8 and r 9 3 express your answer as a decimal to the nearest tenth alan 33.5 33.5 is correct [Applause] as we begin question three alan you have one point jack has no points and here is your question the question is if 2018 equals a b c d base eight what is the value of a plus b plus c plus d in base 10. alan 16 16 is correct [Applause] that brings us to question four alan with two jack with zero and the question is if a and b are positive real numbers such that a plus one over b equals seven what is the least possible value of b plus one over a express your answer as a common fraction jack seven over six i'm sorry that is incorrect ten seconds time's up time has expired the correct answer was four over seven that brings us to the end of the match and alan has answered the most questions correctly alan you will move on to the next round [Applause] jack i look forward to you being able to stop time your youtube series is going to be amazing this brings us into the quarter finals ladies and gentlemen the quarterfinals begin please welcome back from ohio eastern singer [Music] and please welcome from texas luke robitaille uh luke you attend the robotic home school in euless texas um does it stress you out going to a school that has your name in the in the charter no that's good i would feel incredible pressure there's an entire city that i have a name with in uh illinois now you are the returning champion you are the first seed in this year's competition so other than being named national champion what has been your favorite national competition experience uh um well countdown itself is quite fun actually yes so just the math itself is fun that's awesome all right easton let's try your buzzer again luke let's give your buzzer a try all right buzzers are ready you guys look like your pencil hands are strong we are ready to begin the quarterfinals with question one good luck to both of you the question is what is the fewest number of nine inch by nine inch tiles needed yes easton 896. 896 is correct wow [Applause] easton tell me the truth are you a wizard i thought so no my practicing mental math over the past like seven years has helped that's right science beats magic every day of the week all right that brings us to question number two and the question is victor wrote down all the possible combinations of four distinct positive integers less than 10 that sum to 28. how many times did he write the digit eight yes two two times is correct that ties our score we are all tied up as we head into question three and the question is if a rectangular prism has dimensions 79 centimeters by 83 centimeters by 87 centimeters yes easton 498 that is incorrect what is the sum in centimeters of the lengths of all its edges [Music] luke 996 996 centimeters is correct [Music] has two correct answers easton has one correct answer and here is question number four the question is greta's hair grows at a rate of 0.3 millimeters per day an inch is 2.54 times as long as a centimeter how many weeks will it take for yes luke 12. 12 weeks is correct congratulations luke robitaille advances at the end of the match excellent work for both competitors please welcome back from puerto rico jessica juan [Applause] and please welcome to the stage from new jersey daniel sia welcome daniel hello uh daniel comes to us from william anin middle school he is in the eighth grade in basking ridge new jersey um on one of our surveys daniel we asked you if you had a chance to travel back in time what year would you choose you wanted to travel back to the 1970s to see what your parents were like yeah having lived through the 70s i can tell you not good not good a lot of polyester are you at all worried that traveling back in time to meet your parents might alter the course of history and result in you never making it to the national competition that's why i don't consider these questions [Laughter] uh real quick follow-up question do you believe that time travel exists on a closed loop or is branching universes i don't understand these topics neither do i excellent well um welcome and good luck to both of you as we begin the round right after we test your buzzers daniel go ahead and give your buzzer a try excellent and jessica good job all right question number one and the question is if t h o and r are distinct positive integers such that t squared plus h squared equals 25 yes jessica 120. pick up mjolnir because 120 is the correct [Applause] answer that gives jessica one point as we move on to question number two and the question is in a finite list of positive integers each number except for the last number is a proper divisor of the next number in the list if the first number in the list is 1 and the last number is 650 what is the greatest possible sum of the numbers in the list daniel 1054 the correct answer is 1054 and we are tied [Applause] here comes question number three the question is on eco day 12 students volunteer to plant 49 tree saplings if each volunteer plants at least one tree what is the greatest possible value of jessica four four is incorrect what is the greatest possible value of the median number of trees planted by a student daniel six six trees is correct the score is now two for daniel and one for jessica as we move to question number four and the question is let d of k be the number of diagonals in a regular polygon with k sides if d of m plus d of n equals 125 what is the value of m plus n daniel 28 28 is incorrect 10 seconds time's up time has expired the correct answer is 25. this brings us to question five are you both ready all right the question is let n be the greatest composite number less than 100 that does not have a factor that is a perfect square greater than one let d be the sum of the distinct prime factors of n what is the value of n times d jessica 980 i'm sorry i repeat that 980. i'm sorry that is incorrect 10 seconds daniel 2 280. 2280 is correct that will end the match and daniel shia will advance the next round [Applause] we now come to round seven in our quarterfinals please welcome to the stage our third seed daniel yohn from texas andrew kai i'm sorry william chen my cards are out of order ah the internet's gonna just have all kinds of comments about me today um daniel welcome uh i understand that you like watching youtube videos yeah uh what is your favorite youtube show uh clash royale i'm sorry the correct answer is my show tabletop uh we have some aspiring filmmakers here with us today and they'll be showcasing their videos during the math video challenge finals this afternoon so since we are speaking of videos can we have our math video challenge team stand up to be recognized [Applause] awesome uh daniel you are in the eighth grade uh you come to us from uh robert frost middle school you've made the arduous journey from north potomac maryland to be here today uh would you please test your buzzer excellent and william chest your buzzer please great all right gentlemen are we ready all right here we go the question is a hand is a unit of length that is four times as long as an inch how many square hands are in one square yes william 81 81 hands is correct diet you could do this you can do this uh that gives william one and daniel zero let's move on to question number two what is the value of the quantity of the square root of 99 plus the square root of 33 over the quantity the square root yes william 264. that is incorrect over the quantity the square root of 99 plus the square root of 33 all plus the quantity the square root of 99 minus the square root of 33 over the quantity the square root of 99 plus the square root of 33. 10 seconds daniel 4 the correct answer is four and we are tied as we head into question number three and the question is the fifth term of an arithmetic sequence is 13. yes daniel 117. the correct answer is 117. gives daniel two points and william one point it is time for question number four and the question is jacob leonard isaac gottlieb pierre and renee are to be seated at a circular table leonard demands to sit next to jacob isaac refuses to sit next to gottlieb if the seats of the table are rotationally indistinguishable in how many ways can the six mathematicians be seated at the table daniel 24 24 ways is correct daniel young you advance to the next round congratulations thank you william [Applause] round eights competitors are from pennsylvania alan chen and joining us from texas andrew kai [Applause] welcome andrew you are in eighth grade you attend quail valley middle school in sugarland texas um we ask all of the competitors what their career aspirations are we hear all kinds of responses about science and math your response is amazing i love your response you said you want to do a collab with drake yeah i just want to know how you envision your collab with drake it's going to be great do you think you may feature anyone else in the in the collaborate is it just you and drake just us too so no childish gambino he's very hot right now nah yeah it's just you and drake all right i'm i represent childish gambino i'm trying to get him a break that's why i'm pushing him so hard well i really look forward to seeing this collab it's going to be incredible um good luck to both of you let's test your buzzers before we begin the round andrew and alan great i believe we are all set here we go question one and the question is sequences a and b are defined as follows a is 12 14 16 and so on through 2x plus 10 for a positive integer x b is 1002 yes andrew buy 42. 542 is correct [Applause] and i appreciate you buzzing in so quickly i was going to have to stop off for provisions before i got to the end of that question uh andrew you have one alan you have zero this is question number two and the question is on a cold day in chicago the temperature dropped at a constant rate between 6 p.m and 12 a.m yes andrew negative three negative three is correct andrew with two allen waiting to get on the board here is question number three and the question is the first term of a sequence of positive integers is a two-digit number if n represents a term of the sequence then the next term of the sequence is 2n if 2n is yes andrew 17. i'm sorry that's incorrect if 2n is less than 102n minus 100 if 2n is greater than or equal to 100. if the seventh term of this sequence is 68 then what is the fifth term of this sequence 10 seconds alan 84 i'm sorry the correct answer is 92. that brings us to question number four question four and the question is after eating two-thirds of the candies in a jar emma eats 11 more candies yes andrew 66. i'm sorry that is incorrect if the remaining number of candies is one-fourth of the number originally in the jar how many candies were originally in the jar 132 the correct answer is 132 candies [Applause] andrew with two allen with one that makes question number five extremely exciting and the question is the three adjacent squares shown have areas from left to right of one nine and x square units respectively if the segment drawn between vertices a and b is perpendicular to the segment drawn between vertices b and c what yes andrew nine over four uh one more time please nine over four judges no i'm sorry that is incorrect if the segment drawn between vertices a and b is perpendicular to the segment drawn between vertices b and c what is the value of x express your answer as a common fraction 10 seconds time's up time has expired the correct answer is 81 over 16. that ends the match and with two points andrew kai advances to the next round big round of applause for all of our competitors today [Applause] we are now in the semi-finals the semi-finals have new rules in the semi-finals you need four correct answers to advance to the finals i would like to invite the coaches of these four semifinalists to come down to the front we have reserved excellent chairs for you they have been chosen from dozens of chairs all over the hotel to ensure that your comfort and security is paramount a round of applause for our coaches and in our first semi-final round please welcome our number one seed luke robitaille from texas and our number four seed from new jersey daniel sia welcome back gentlemen let's test your buzzers daniel go ahead great luke good work all right good luck to both of you let us begin the first to four correct answers we'll advance to the finals our first question is what is the value of the quantity the quantity the square root of 1.06 minus 1 over 3 yes luke 1.02 1.02 is correct luke with one correct answer is 25 of the way and that is the extent of my math knowledge the next question is if x is a real number such that x minus seven times the square root of the quantity yes luke 49 49 is incorrect x minus 7 times the square root of the quantity x plus 4 equals 14. what is the value of x daniel 121 i'm sorry the correct answer is 77. i'm not sure if that was sarcastic thundersticking uh enthusiastic thundersticking very good all right give it up for these guys all four of these guys all right our next question is a positive integer p has the property that p is 11 times the sum of its digits what is the value of p yes 198 198 is correct good work [Applause] luke with two and daniel waiting to get on the board as we go on to our next question the question is if n star is the product of all positive integers less than or equal to n that are powers of 2. what is the value of 20 star minus 18 star plus 16 star minus 14 star plus 12 star minus 10 star plus 8 star minus 6 star plus 4 star yes daniel 1022 1022 is correct and daniel is on the board the score is luke robitaille two daniel sia one and the next question is segments a c and d f intersect parallel lines l m and n as shown the lengths of segments a d b e and c f are 10 12 and 15 units respectively and the area of trapezoid adfc is 80 square units if a line p parallel to line d f passes through b and intersects segment c f at x what is the area of triangle b yes luke 144 over 25 that is correct luke with three daniel with one and our next question is how many positive integers less than 100 are divisible by exactly one of the integers two five and seven yes daniel 64. 64 is incorrect i'm sorry ten seconds luke 49 49 integers is correct luke robitaille you advance to the finals [Applause] our last semi-final match up is andrew kai from texas and daniel yan from maryland [Applause] welcome back seems feels like you were just here um daniel let's give your buzzer a work great and andrew all right are you gentlemen ready yep all right here we go first to four advances to face luke in the finals and the question is if 26 times 23 plus 34 times 23 plus yes andrew 67 67 is correct andrew has one daniel has zero and here comes our next question the question is on a camping trip bobby brought seven sandwiches charlotte brought six sandwiches davis brought nine sandwiches and ashton brought none but they shared the food equally among all four of them to pay for the sandwiches bobby charlotte and davis gave her ashton gives them 20 yes daniel nine i'm sorry nine is incorrect charlotte and davis gave her ashton gives them 22 dollars total to split fairly in proportion yes andrew 12. 12 is incorrect how much of ashton's share each contributed how many dollars will davis get the answer is 14 i want to know why you bring that many sandwiches on a camping trip and expect the lettuce to stay crisp the entire time it is time for our next question and the question is mary is five years younger than jill five years ago the sum of their yes andrew thirty thirty is correct andrew is halfway daniel waiting to get on the board it is time for our next question and the question is integers x and y are chosen at random so that negative 5 is less than or equal to x is less than or equal to five and yes andrew 32 over 121 i'm sorry that is incorrect five is less than or equal to y is less than or equal to five what is the probability that the quantity x plus y squared is greater than x squared plus y squared express your answer as a common fraction 10 seconds daniel 50 over 121. 50 over 121 is correct [Applause] daniel with one andrew with two and the next question is three positive numbers a b and c form a geometric sequence in that order let s equal a plus b plus c and r equal one over a plus one over b plus one over c if yes andrew four four is correct andrew has three correct answers daniel has one correct answer let us move on to our next question and the question is what is the ratio of the number of four-digit palindromes to the number of seven yes daniel 100 i'm sorry 100 time i'm sorry 100 is incorrect what is the ratio of the number of four-digit palindromes to the number of seven-digit palindromes express your answer yes andrew one over one hundred one over one hundred is correct congratulations andrew ladies and gentlemen our final competitors please welcome back luke robitaille from texas taking on andrew kai from texas we have an all texas final [Applause] foreign [Applause] all right gentlemen are we ready yes andrew let's try out your buzzer great luke the buzzers are functional the mathletes are ready it is time to begin the finals and here is your first question the question is this figure shows three squares whose side lengths are 3 12 and 4 units the diagonal segment divides the largest square into two regions one of which is gray what is the ratio of the area of the gray region to the total area yes luke 9 over 19 9 over 19 is correct that gives luke one correct answer and andrew is waiting here is the next question the question is two lines in the coordinate plane have y intercepts of two and eight the two lines intersect at a point nine comma y what is the absolute difference between the slopes of the two lines express your answer as a common fraction andrew two over three two over three is correct we are all tied up at one correct answer apiece and the next question is dan is thinking of a two-digit positive integer x when x is divided by three the remainder is two yes andrew 87 87 is incorrect when x is divided by three the remainder is two when x is divided by four the remainder is one what is the greatest possible value of x luke 89 89 is correct our score is luke robitaille with two andrew kai with one and it is time for our next question the question is a salad bar charges 75 cents per ounce of food clara makes a salad with 2 cups spinach 1 3 cup walnuts and 1 4 cup dressing yes andrew nine nine dollars is correct [Applause] we are all tied up at two correct answers apiece all right are you both ready yes you guys are doing amazing thank you here is your next question the question is cat uses each digit from zero through nine exactly once to create four positive integers consisting of a one-digit integer a two-digit integer a three-digit integer and a four-digit integer if each of the four integers is divisible by nine what is the greatest possible value of the four digit number luke eight seven three zero eight seven three zero is correct luke has three correct answers andrew has two correct answers here is your next question the question is the first three terms of an infinite arithmetic sequence are 3.46 2.47 and 1.48 in that order what is the first integer term in this sequence luke negative 50. negative 50 is correct [Applause] ladies and gentlemen it is my great pleasure and honor to introduce to you our first ever repeat champion luke robitaille

Channel: MATHCOUNTS Foundation

Views: 2,917,322

Keywords: MATHCOUNTS, math, STEM, middle school, Wil Wheaton, Countdown Round, math competition

Id: dSnOLW_W6og

Length: 62min 5sec (3725 seconds)

Published: Wed Jun 13 2018