Practice Mode. Problem Sets. System theme. Free AMC trainer and math learning: AMC practice problems, problem sets, mock tests with real questions from the AMC 8, AMC 10, AMC 12, AIME, and more.2013 AMC 8 Problems/Problem 24; 2013 AMC 8 Problems/Problem 25; See also. 2013 AMC 8 : Preceded by 2012 AMC 8: AMC 8: Followed by 2014 AMC 8: Mathematics competitions;Problem 1. Ike and Mike go into a sandwich shop with a total of to spend. Sandwiches cost each and soft drinks cost each. Ike and Mike plan to buy as many sandwiches as they can, and use any remaining money to buy soft drinks.Problems with Professional Carpet Installation - There are certain problems associated with professional carpet installation. Visit HowStuffWorks to learn more. Advertisement As we...AMC 8. Most people don’t realize that making progress on the first 10 problems is actually a significant achievement! Looking to try out a few practice problems and get your math gears turning? Check out MAA AMC's guided practice and worksheets.2015 AMC 8 Results Announced. 2014 AMC 8 Winners for the U.S. Ivy League Education Center. The Hardest Problems on the 2018 AMC 8 are Nearly Identical to Former Problems on the AMC 8, 10, 12, and MathCounts. The Hardest Problems on the 2017 AMC 8 are Extremely Similar to Previous Problems on the AMC 8/10/12 and the …The original problem and choices from the 2011 AMC 8 contest (A) 12 1 2 (B) 20 (C) 25 (D) 33 1 3 (E) 37 1 2 2011 AMC 8, Problem #7— “Find the shaded portion of each square separately. ” Problem number Hint Solution Answer (C): The upper left and the lower right squares are each one-fourth shaded, for a total of one-half square.AMC 8 Mock Test Problems Problem 1 s Ft Eu Fv E® F trtr E trts L (A) Fsrss (B) Fsrsr (C) r (D) srsr (E) srss Problem 2 What is the number halfway between 5 5 : and 5 6 4? (A) 5 5 : 4 (B) 5 < 4 (C) 5 5 < (D) = 5 : 4 (E) 5 = Problem 3 A triangular corner with side length s pn L qn L Ú is cut from equilateral triangle mno of side length 3. 2019 AMC 8 Problems. 2019 AMC 8 Printable versions: Wiki • AoPS Resources • PDF: Instructions. This is a 25-question, multiple choice test. Each question is ... 2020 AMC 8 The problems in the AMC-Series Contests are copyrighted by American Mathematics Competitions at Mathematical Association of America (www.maa.org). For more practice and resources, visit ziml.areteem.org. Q u e s t i o n . 1. N o t ye t a n sw e r e d. P o in t s o u t o f 1.Jan 2, 2022 · The AMC 8 is administered from January 18, 2022 until January 24, 2022. According to the AMC policy, "problems and solutions are not discussed in any online or public forum until January 25," as emphasized in 2021-2022 AMC 8 Teacher's Manual. “master-solution˙final” — 2016/9/13 — 15:30 — page 6 — #5 2016 AMC 8 Solutions 6 20. Answer (A): If b = 1, then a = 12 and c = 15, and the least common multiple of a and c is 60. If b > 1, then any prime factor of b must also be a factor of both 12 and 15, and thus the only possible value is b=3.In this case, a must be a multiple of 4 and a divisor of 12, so a = 4 …Problem 7. The integers from to inclusive, can be arranged to form a -by-square in which the sum of the numbers in each row, the sum of the numbers in each column, and the sum of the numbers along each of the main diagonals are all the same. What is the value of this common sum? Solution. Problem 8. What is the value of Solution. Problem 9Solution. Problem 23. A or is placed in each of the nine squares in a -by-grid. Shown below is a sample configuration with three s in a line. How many configurations will have three s in a line and three s in a line?. Solution. Problem 24. The figure below shows a polygon , consisting of rectangles and right triangles.When cut out and folded on the dotted lines, …AMC 8 American Mathematics Contest 8 Tuesday, November 17, 2015 INSTRUCTIONS 1. DO NOT OPEN THIS BOOKLET UNTIL YOUR PROCTOR TELLS YOU. 2. This is a twenty-five question multiple choice test. For each question, only one answer choice is correct. 3. Mark your answer to each problem on the AMC 8 Answer Form with a #2 …Problem 1. Ike and Mike go into a sandwich shop with a total of to spend. Sandwiches cost each and soft drinks cost each. Ike and Mike plan to buy as many sandwiches as they can, and use any remaining money to buy soft drinks.2017 AMC 8 Problems Problem 1 Which of the following values is largest? Problem 2 Alicia, Brenda, and Colby were the candidates in a recent election for student president. The pie chart below shows how the votes were distributed among the three candidates. If Brenda received 36 votes, then how many votes were cast all together? Problem 34. The numbers from 1 to 49 are arranged in a spiral pattern on a square grid, beginning at the center. The first few numbers have been entered into the grid below.Are you prepared for travel problems on your vacation? Check out these tips to help you prevent a vacation nightmare before it starts. Daye Deura When going on a hard-earned vacati...The AMC 8 is administered from November 12, 2019 until November 18, 2019. According to the AMC policy, students, teachers, and coaches are not allowed to discuss the contest questions and solutions until after the end of the competition window, as emphasized in 2019 AMC 8 Teacher's Manual. We posted the 2019 AMC 8 Problems …Teachers are encouraged to share copies of the problem booklet and official solutions with their students for educational purposes. All problems should be credited to the MAA AMC (for example, “2017 AMC 12 B, Problem #21”). The publication, reproduction, or communication of the competition’s problems or solutionsPractice Mode. Problem Sets. System theme. Free AMC trainer and math learning: AMC practice problems, problem sets, mock tests with real questions from the AMC 8, AMC 10, AMC 12, AIME, and more.2012 AMC 8 Problems/Problem 22; 2012 AMC 8 Problems/Problem 23; 2012 AMC 8 Problems/Problem 24; 2012 AMC 8 Problems/Problem 25; See also. 2012 AMC 8 : Preceded by 2011 AMC 8: AMC 8: Followed by 2013 AMC 8: Mathematics competitions; Mathematics competition resources; Math books; 2019 AMC 8 Problems Problem 1 Ike and Mike go into a sandwich shop with a total of $30.00 to spend. Sandwiches cost $4.50 each and soft drinks cost $1.00 each. Ike and Mike plan to buy as many sandwiches as they can, and use any remaining money to buy soft drinks. Counting both sandwiches and soft drinks, how many items will they buy? Problem 2 If you own a GE dishwasher, you may encounter some common problems that can disrupt its performance. While these issues can be frustrating, many of them can be resolved with simple...AMC 8 American Mathematics Contest 8 Tuesday, November 15, 2011 INSTRUCTIONS 1. DO NOT OPEN THIS BOOKLET UNTIL YOUR PROCTOR TELLS YOU. 2. This is a twenty-five question multiple choice test. For each question, only one answer choice is correct. 3. Mark your answer to each problem on the AMC 8 Answer Form with a #2 …The first link contains the full set of test problems. The rest contain each individual problem and its solution. 2001 AMC 8 Problems. 2001 AMC 8 Answer Key. 2001 AMC 8 Problems/Problem 1. 2001 AMC 8 Problems/Problem 2. 2001 AMC 8 Problems/Problem 3. 2001 AMC 8 Problems/Problem 4. 2001 AMC 8 Problems/Problem 5. The first link contains the full set of test problems. The rest contain each individual problem and its solution. 2005 AMC 8 Problems. 2005 AMC 8 Answer Key. 2005 AMC 8 Problems/Problem 1. 2005 AMC 8 Problems/Problem 2. 2005 AMC 8 Problems/Problem 3. 2005 AMC 8 Problems/Problem 4. 2005 AMC 8 Problems/Problem 5. Resources Aops Wiki 2018 AMC 8 Problems Page. Article Discussion View source History. Toolbox. Recent changes Random page Help What links here Special pages. Search. ONLINE AMC 8 PREP WITH AOPS Top scorers around the country use AoPS. Join training courses for beginners and advanced students.Problem 1. What is the value of . Solution. Problem 2. The sum of three numbers is The first number is times the third number, and the third number is less than the second number. What is the absolute value of the difference between the first and second numbers? Solution. Problem 3. Five rectangles, , , , , and , are arranged in a square as ...Don’t waste your time and money on plumbing issues that you don’t know how to fix. Here are the most common plumbing problems and how to avoid them. If your pipes or sinks are drip... night they each solved half of the problems in their homework assign-ment alone and then solved the other half together. Chloe had correct answers to only 80% of the problems she solved alone, but overall 88% of her answers were correct. Zoe had correct answers to 90% of the problems she solved alone. What was Zoe’s overall percentage of 2012 AMC 8 Problems/Problem 22; 2012 AMC 8 Problems/Problem 23; 2012 AMC 8 Problems/Problem 24; 2012 AMC 8 Problems/Problem 25; See also. 2012 AMC 8 : Preceded by 2011 AMC 8: AMC 8: Followed by 2013 AMC 8: Mathematics competitions; Mathematics competition resources; Math books;An estimated three out of four people wear some form of corrective lenses, according to the Vision Impact Institute. Even though so many people wear glasses and contacts, correctiv...This Solutions Pamphlet gives at least one solution for each problem on this year’s exam and shows that all ... AMC 8 American Mathematics Contest 8 Tuesday, November 14, 2017 MATHEMATICAL ASSOCIATION OF AMERICA. 2017 AMC8 Solutions 2 1. Answer (A): The values of the expressions are, in order, 10, 8, 9, 9, and 0.This is the same problem as if we made the spinner A make the tens digit and spinner B make the ones digit. If the tens digit is 5,6,7, or 8, and the ones digit is 1,2,3, or 4, the only possible ways to get a perfect square is 6,4 or 8,1. There are 4x4=16 possible combinations that are equally likely, and 2 of them satisfy the property.The first link contains the full set of test problems. The rest contain each individual problem and its solution. 2001 AMC 8 Problems. 2001 AMC 8 Answer Key. 2001 AMC 8 Problems/Problem 1. 2001 AMC 8 Problems/Problem 2. 2001 AMC 8 Problems/Problem 3. 2001 AMC 8 Problems/Problem 4. 2001 AMC 8 …Jan 24, 2023 ... Join LIVE, by Po-Shen Loh for review sessions to dive into problems from 2023 AMC 8! The sessions will take place 1/24/23 and 1/26/23 at 8pm ...Hello everybody! I've been receiving a lot of requests to write more competition-related articles, especially because the AMC is approaching pretty quickly: the exams will be hosted on February 4 and February 10, 2021. Today, I thought I'd take the opportunity to curate a set of my 40 favorite problems to serve as a resource for your AMC prep, grouped by category. I aimed this compilation at ... Problem 20. The grid below is to be filled with integers in such a way that the sum of the numbers in each row and the sum of the numbers in each column are the same. Four numbers are missing. The number in the lower left corner is larger than the other three missing numbers. What is the smallest possible value of ? 2 2019 MAA AMC 8 Solutions 1.Ike and Mike go into a sandwich shop with a total of $30.00 to spend. Sandwiches cost $4.50 each and soft drinks cost $1.00 each. Ike and Mike plan to buy as many sandwiches as they can and use any remaining money to buy soft drinks. Counting both soft drinks and sandwiches, how many items will they buy? 2016 AMC 8 Problems. 2016 AMC 8 Printable versions: Wiki • AoPS Resources • PDF: Instructions. This is a 25-question, multiple choice test. Each question is ... Solution 3. Notice that the area of the figure is equal to the area of the square subtracted by the triangles that are half the area of each square, which is . The total area of the triangles not in the figure is , so the answer is . ~hh99754539. Problem 20. The grid below is to be filled with integers in such a way that the sum of the numbers in each row and the sum of the numbers in each column are the same. Four numbers are missing. The number in the lower left corner is larger than the other three missing numbers. What is the smallest possible value of ?2011 AMC 8 Problems/Problem 22; 2011 AMC 8 Problems/Problem 23; 2011 AMC 8 Problems/Problem 24; 2011 AMC 8 Problems/Problem 25; See also. 2011 AMC 8 : Preceded by 2010 AMC 8: AMC 8: Followed by 2012 AMC 8: Mathematics competitions; Mathematics competition resources; Math books;If you’ve read Lifehacker for more than five minutes, you probably know we have a ton of resources on how to learn to code. You’ll also know it’s still hard. Part of the problem is...Problem 1. Ike and Mike go into a sandwich shop with a total of to spend. Sandwiches cost each and soft drinks cost each. Ike and Mike plan to buy as many sandwiches as they can, and use any remaining money to buy soft drinks.AMC 8 is a middle school mathematics competition that tests problem-solving skills. Find out how to register, prepare, and access resources for the AMC 8 …Dec 28, 2022 ... Solving problem #8 from the 2022 AMC 8 test.Millionaires have problems you don't, like fake friends who hang out with them just for their money and people suing them for money. By clicking "TRY IT", I agree to receive newsle...2011 AMC 8, Problem #7— “Find the shaded portion of each square separately.” Solution Answer (C): The upper left and the lower right squares are each one-fourth shaded, fora total of one-half square. The shaded portions of the upper right and lower left squares makeu p one-half square.S o the total shaded area isSolution 2 (Coordinate Geometry) Let the midpoint of segment be the origin. Evidently, point and . Since points and share -coordinates with and respectively, it suffices to find the -coordinate of (which will be the height of the rectangle) and multiply this by (which we know is ). The radius of the semicircle is , so the whole circle has ... Resources Aops Wiki AMC 12 Problems and Solutions Page. Article Discussion View source History. Toolbox. Recent changes Random page Help What links here Special pages. AMC 10 Problems and Solutions - AoPS Wiki. Art of Problem Solving. AoPS Online. Math texts, online classes, and more. for students in grades 5-12. Visit AoPS Online ‚. Books for Grades 5-12 Online Courses. Beast Academy. Engaging math books and online learning.20 20 AMC 8 Problems Problem 1 Luka is making lemonade to sell at a school fundraiser. His recipe requires 4 times as much water as sugar and twice as much sugar as lemon juice. He uses 3 cups of lemon juice. How many cups of water does he need? Problem 2 Four friends do yardwork for their neighbors over the weekend, earning $15, $20, $25, andHeredity. It is quite possible that thyroid problems develop more frequently in humans whose ancestors had any throat diseases or thyroid disease itself. In fact, one cannot claim ...When dealing with organizational problems, managers should first determine what the core problem is and how strong of an effect it has on the workplace environment.Heredity. It is quite possible that thyroid problems develop more frequently in humans whose ancestors had any throat diseases or thyroid disease itself. In fact, one cannot claim ...Solution 2. Let and the height of . We can extend to form a parallelogram, which would equal . The smaller parallelogram is times . The smaller parallelogram is of the larger parallelogram, so the answer would be , since the triangle is of the parallelogram, so the answer is . By babyzombievillager with credits to many others who helped with ...This is the same problem as if we made the spinner A make the tens digit and spinner B make the ones digit. If the tens digit is 5,6,7, or 8, and the ones digit is 1,2,3, or 4, the only possible ways to get a perfect square is 6,4 or 8,1. There are 4x4=16 possible combinations that are equally likely, and 2 of them satisfy the property.Solution 2. Let and the height of . We can extend to form a parallelogram, which would equal . The smaller parallelogram is times . The smaller parallelogram is of the larger parallelogram, so the answer would be , since the triangle is of the parallelogram, so the answer is . By babyzombievillager with credits to many others who helped with ...This Solutions Pamphlet gives at least one solution for each problem on this year’s exam and shows that all ... AMC 8 American Mathematics Contest 8 Tuesday, November 14, 2017 MATHEMATICAL ASSOCIATION OF AMERICA. 2017 AMC8 Solutions 2 1. Answer (A): The values of the expressions are, in order, 10, 8, 9, 9, and 0.Solution 1. Let the centers of the circles containing arcs and be and , respectively. Extend and to and , and connect point with point . We can clearly see that is an equilateral triangle, because the problem states that . We can figure out that and because they are of a circle. The area of the figure is equal to minus the combined area of the ...Nov 17, 2020 · On the 2020 AMC 8, there are 8 counting problems, 15 arithmetic and algebra problems, 1 geometry problem and 1 number theory problem. Surprisingly, there are no probability problems. This year's AMC 8 was harder than ever before. All the problems are word problems, and require critical thinking along with advanced math skills. Hello everybody! I've been receiving a lot of requests to write more competition-related articles, especially because the AMC is approaching pretty quickly: the exams will be hosted on February 4 and …The first link contains the full set of test problems. The rest contain each individual problem and its solution. 2001 AMC 8 Problems. 2001 AMC 8 Answer Key. 2001 AMC 8 Problems/Problem 1. 2001 AMC 8 Problems/Problem 2. 2001 AMC 8 Problems/Problem 3. 2001 AMC 8 Problems/Problem 4. 2001 AMC 8 …Having a patio umbrella is a great way to enjoy the outdoors while staying protected from the sun. However, like any other outdoor equipment, patio umbrellas can encounter problems...AMC 8 American Mathematics Contest 8 Tuesday, November 13, 2012 INSTRUCTIONS 1. DO NOT OPEN THIS BOOKLET UNTIL YOUR PROCTOR TELLS YOU. 2. This is a twenty-five question multiple choice test. For each question, only one answer choice is correct. 3. Mark your answer to each problem on the AMC 8 Answer Form with a #2 pencil.2019 AMC 8 Problems Problem 1 Ike and Mike go into a sandwich shop with a total of to spend. Sandwiches cost each and soft drinks cost each. Ike and Mike plan to buy as many sandwiches as they can and use the remaining money to buy soft drinks. Counting both soft drinks and sandwiches, how many items will they buy? Problem 2An estimated three out of four people wear some form of corrective lenses, according to the Vision Impact Institute. Even though so many people wear glasses and contacts, correctiv...The AMC 8 is a math contest organized by the Mathematical Association of America (MAA). The AMC 8 contest contains 25 multiple choice questions that must be completed within 40 minutes. There is no negative marking on the test, so remember to put an answer for every problem (even if you have to guess). Who can take the AMC 8.American Mathematics Competitions . Author: Marcio Sejas Created Date: 11/19/2020 1:40:20 PM4. The numbers from 1 to 49 are arranged in a spiral pattern on a square grid, beginning at the center. The first few numbers have been entered into the grid below.2011 AMC 8 Problems/Problem 22; 2011 AMC 8 Problems/Problem 23; 2011 AMC 8 Problems/Problem 24; 2011 AMC 8 Problems/Problem 25; See also. 2011 AMC 8 : Preceded by 2010 AMC 8: AMC 8: Followed by 2012 AMC 8: Mathematics competitions; Mathematics competition resources; Math books;We collected all problems from past AMC 8 exams (1999-2023) and AJHSME (1985–1998), which form our “big data” system. The AJHSME (American Junior High School Mathematics Examination) was the former name of the AMC 8, before 1999. We used data mining and predictive analytics to examine the types, styles, and …Solution 3. Since each person needs to have at least two apples, we can simply give each person two, leaving apples. For the remaining apples, if Alice is going to have apples, Becky is going to have apples, and Chris is going to have apples, we have indeterminate equation . Currently, we can see that where is an integer, and when equals any ...Solution 1. First, we calculate that there are a total of possibilities. Now, we list all of two-digit perfect squares. and are the only ones that can be made using the spinner. Consequently, there is a probability that the number formed by the two spinners is a perfect square. ~MathFun1000.AMC 8 American Mathematics Contest 8 Tuesday, November 15, 2016 INSTRUCTIONS 1. DO NOT OPEN THIS BOOKLET UNTIL YOUR PROCTOR TELLS YOU. 2. This is a twenty-five question multiple choice test. For each question, only one answer choice is correct. 3. Mark your answer to each problem on the AMC 8 Answer Form with a #2 …Solution 1. Clearly, the amount of money Ricardo has will be maximized when he has the maximum number of nickels. Since he must have at least one penny, the greatest number of nickels he can have is , giving a total of cents. Analogously, the amount of money he has will be least when he has the greatest number of pennies; as he must have at ...We collected all problems from past AMC 8 exams (1999-2023) and AJHSME (1985–1998), which form our “big data” system. The AJHSME (American Junior High School Mathematics Examination) was the former name of the AMC 8, before 1999. We used data mining and predictive analytics to examine the types, styles, and …Jan 2, 2022 · The AMC 8 is administered from January 18, 2022 until January 24, 2022. According to the AMC policy, "problems and solutions are not discussed in any online or public forum until January 25," as emphasized in 2021-2022 AMC 8 Teacher's Manual. 2013 AMC 8 Problems/Problem 22; 2013 AMC 8 Problems/Problem 23; 2013 AMC 8 Problems/Problem 24; 2013 AMC 8 Problems/Problem 25; See also. 2013 AMC 8 : Preceded by 2012 AMC 8: AMC 8: Followed by 2014 AMC 8: Mathematics competitions; Mathematics competition resources; Math books; The first link contains the full set of test problems. The rest contain each individual problem and its solution. 2022 AMC 8 Problems. 2022 AMC 8 Answer Key. Problem 1. Problem 2. Problem 3. Problem 4. Problem 5.
2018 AMC 8 Problems. 2018 AMC 8 Printable versions: Wiki • AoPS Resources • PDF: Instructions. This is a 25-question, multiple choice test. Each question is ... . Chime tax refund 2023
Appliances play a crucial role in our daily lives, making household chores more efficient and convenient. However, like any other mechanical device, A&E appliances can develop prob... 2023 AMC 8 Problems. 2023 AMC 8 Printable versions: Wiki • AoPS Resources • PDF: Instructions. This is a 25-question, multiple choice test. Each question is ... AMC 8 American Mathematics Contest 8 Tuesday, November 15, 2011 INSTRUCTIONS 1. DO NOT OPEN THIS BOOKLET UNTIL YOUR PROCTOR TELLS YOU. 2. This is a twenty-five question multiple choice test. For each question, only one answer choice is correct. 3. Mark your answer to each problem on the AMC 8 Answer Form with a #2 pencil.Coleman furnaces are known for their reliability and durability. However, like any other appliance, they can experience problems from time to time. One of the most common issues wi...2018 AMC 8 Problems. 2018 AMC 8 Printable versions: Wiki • AoPS Resources • PDF: Instructions. This is a 25-question, multiple choice test. Each question is ...Past AMC 8 and AMC 10 Problems. Welcome to our past problem and solution archive. We've built a smartphone-optimized interface for viewing and working on the past exams on the go. We also have printable PDF versions of each past test. Enjoy these past AMC contests!Resources Aops Wiki 2023 AMC 8 Problems Page. Article Discussion View source History. Toolbox. Recent changes Random page Help What links here Special pages. Search. ONLINE AMC 8 PREP WITH AOPS Top scorers around the country use AoPS. Join training courses for beginners and advanced students.Click here to download. The Mastering AMC 8 book covers the most important concepts on the AMC 8 exam (and MATHCOUNTS) and includes 100s of examples and practice problems with detailed video solutions. This book covers the following topics: Combinatorics. Algebra. Number Theory.Resources Aops Wiki 2023 AMC 8 Problems Page. Article Discussion View source History. Toolbox. Recent changes Random page Help What links here Special pages. Search. ONLINE AMC 8 PREP WITH AOPS Top scorers around the country use AoPS. Join training courses for beginners and advanced students.If school is canceled on the day that the AMC 8 was scheduled, the competition manager can administer the AMC 8 on a different day as long as it falls within the AMC 8 competition period, Jan. 17-23, 2023. The AMC 8 cannot be administered after the final day of the competition period. During the last two cycles, we temporarily allowed remote ...While composite decking certainly does have some advantages, it also has a number of problems that the average homeowner may be unaware of. Expert Advice On Improving Your Home Vid...Click here to download. The Mastering AMC 8 book covers the most important concepts on the AMC 8 exam (and MATHCOUNTS) and includes 100s of examples and practice problems with detailed video solutions. This book covers the following topics: Combinatorics. Algebra. Number Theory.Our online AMC 10 Problem Series course has been instrumental preparation for thousands of top AMC 10 scorers over the past decade. LEARN MORE AMC 10 Problems and Solutions. AMC 10 problems and solutions. Year Test A Test B 2023: AMC 10A: AMC 10B: 2022: AMC 10A: AMC 10B: 2021 Fall: AMC 10A: AMC 10B: 2021 Spring: AMC 10A: …The first link contains the full set of test problems. The rest contain each individual problem and its solution. 2001 AMC 8 Problems. 2001 AMC 8 Answer Key. 2001 AMC 8 Problems/Problem 1. 2001 AMC 8 Problems/Problem 2. 2001 AMC 8 Problems/Problem 3. 2001 AMC 8 Problems/Problem 4. 2001 AMC 8 Problems/Problem 5.2018 AMC 8 problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. 2018 AMC 8 Problems. 2018 AMC 8 Answer Key. Problem 1..
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