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• 15:07, 11 July 2021 (diff | hist) . . (+209)‎ . . N 2021 JMPSC Invitationals Problems/Problem 11 ‎ (Created page with "==Problem== For some <math>n</math>, the arithmetic progression <cmath>4,9,14,\ldots,n</cmath> has exactly <math>36</math> perfect squares. Find the maximum possible value of...")
• 15:07, 11 July 2021 (diff | hist) . . (+441)‎ . . N 2021 JMPSC Invitationals Problems/Problem 10 ‎ (Created page with "==Problem== A point <math>P</math> is chosen in isosceles trapezoid <math>ABCD</math> with <math>AB=4</math>, <math>BC=20</math>, <math>CD=28</math>, and <math>DA=20</math>. I...")
• 15:07, 11 July 2021 (diff | hist) . . (+249)‎ . . N 2021 JMPSC Invitationals Problems/Problem 9 ‎ (Created page with "==Problem== In <math>\triangle ABC</math>, let <math>D</math> be on <math>\overline{AB}</math> such that <math>AD=DC</math>. If <math>\angle ADC=2\angle ABC</math>, <math>AD=1...")
• 15:06, 11 July 2021 (diff | hist) . . (+2)‎ . . 2021 JMPSC Invitationals Problems/Problem 8 ‎ (→‎Problem)
• 15:05, 11 July 2021 (diff | hist) . . (+197)‎ . . N 2021 JMPSC Invitationals Problems/Problem 8 ‎ (Created page with "==Problem== Let <math>x</math> and <math>y</math> be real numbers that satisfy <cmath>(x+y)^2(20x+21y) = 12</cmath> (x+y)(20x+21y)^2 = 18.<math></math> Find <math>21x+20y</mat...")
• 15:05, 11 July 2021 (diff | hist) . . (+411)‎ . . N 2021 JMPSC Invitationals Problems/Problem 7 ‎ (Created page with "==Problem== In a <math>3 \times 3</math> grid with nine square cells, how many ways can Jacob shade in some nonzero number of cells such that each row, column, and diagonal c...")
• 15:04, 11 July 2021 (diff | hist) . . (+487)‎ . . N 2021 JMPSC Invitationals Problems/Problem 6 ‎ (Created page with "==Problem== Five friends decide to meet together for a party. However, they did not plan the party well, and at noon, every friend leaves their own house and travels to one of...")
• 15:03, 11 July 2021 (diff | hist) . . (0)‎ . . 2021 JMPSC Invitationals Problems/Problem 5 ‎ (→‎Problem)
• 15:02, 11 July 2021 (diff | hist) . . (+434)‎ . . N 2021 JMPSC Invitationals Problems/Problem 5 ‎ (Created page with "==Problem== An <math>n</math>-pointed fork is a figure that consists of two parts: a handle that weighs <math>12</math> ounces and <math>n</math> "skewers" that each weigh a n...")
• 15:02, 11 July 2021 (diff | hist) . . (0)‎ . . N File:Invites5.png ‎ (current)
• 15:01, 11 July 2021 (diff | hist) . . (-1)‎ . . 2021 JMPSC Invitationals Problems/Problem 4 ‎ (→‎Problem)
• 15:01, 11 July 2021 (diff | hist) . . (+340)‎ . . N 2021 JMPSC Invitationals Problems/Problem 4 ‎ (Created page with "==Problem== Let <math>(x_n)_{n\geq 0}</math> and <math>(y_n)_{n\geq 0}</math> be sequences of real numbers such that <math>x_0 = 3</math>, <math>y_0 = 1</math>, and, for all...")
• 15:00, 11 July 2021 (diff | hist) . . (+238)‎ . . N 2021 JMPSC Invitationals Problems/Problem 3 ‎ (Created page with "==Problem== There are exactly <math>5</math> even positive integers less than or equal to <math>100</math> that are divisible by <math>x</math>. What is the sum of all possibl...")
• 14:59, 11 July 2021 (diff | hist) . . (+201)‎ . . N 2021 JMPSC Invitationals Problems/Problem 2 ‎ (Created page with "==Problem== Two quadrilaterals are drawn on the plane such that they share no sides. What is the maximum possible number of intersections of the boundaries of the two quadrila...")
• 14:59, 11 July 2021 (diff | hist) . . (+176)‎ . . N 2021 JMPSC Invitationals Problems/Problem 1 ‎ (Created page with "==Problem== The equation <math>ax^2 + 5x = 4,</math> where <math>a</math> is some constant, has <math>x = 1</math> as a solution. What is the other solution? ==Solution== asdf")
• 14:58, 11 July 2021 (diff | hist) . . (+1,625)‎ . . N 2021 JMPSC Invitationals Problems ‎ (Created page with "#This is a fifteen question free-response test. Each question has exactly one integer answer. #You have 80 minutes to complete the test. #You will receive 15 points for each c...")
• 14:50, 11 July 2021 (diff | hist) . . (+61)‎ . . N 2021 JMPSC Invitationals Answer Key ‎ (Created page with "#4 #16 #47 #307 #22 #271 #17 #79 #24 #59 #8459 #83 #-8 #24 #8") (current)
• 13:57, 11 July 2021 (diff | hist) . . (+498)‎ . . 2021 JMPSC Accuracy Problems/Problem 11 ‎ (→‎Solution 3 (A Little Bashy))
• 13:43, 11 July 2021 (diff | hist) . . (+1,312)‎ . . N 2021 JMPSC Invitationals ‎ (Created page with "'''2021 JMPSC Invitationals (Middle School)''' problems and solutions. The test was held on July 10th, 2021. *2021 JMPSC Invitationals Problems *2021 JMPSC Invitationa...")
• 13:23, 11 July 2021 (diff | hist) . . (+31)‎ . . JMPSC Problems and Solutions ‎
• 23:31, 10 July 2021 (diff | hist) . . (-85)‎ . . 2021 JMPSC Sprint Problems ‎
• 23:31, 10 July 2021 (diff | hist) . . (-85)‎ . . 2021 JMPSC Accuracy Problems ‎
• 23:27, 10 July 2021 (diff | hist) . . (-33)‎ . . JMPSC Problems and Solutions ‎ (→‎Resources)
• 23:20, 10 July 2021 (diff | hist) . . (+675)‎ . . 2021 JMPSC Sprint Problems/Problem 20 ‎ (→‎Solution)
• 23:18, 10 July 2021 (diff | hist) . . (+17)‎ . . 2021 JMPSC Accuracy Problems/Problem 12 ‎ (→‎Solution)
• 23:17, 10 July 2021 (diff | hist) . . (+17)‎ . . 2021 JMPSC Accuracy Problems/Problem 12 ‎ (→‎Solution)
• 23:17, 10 July 2021 (diff | hist) . . (+1,134)‎ . . 2021 JMPSC Accuracy Problems/Problem 12 ‎ (→‎Solution)
• 23:16, 10 July 2021 (diff | hist) . . (0)‎ . . N File:Accuracy12sol.jpeg ‎ (current)
• 22:54, 10 July 2021 (diff | hist) . . (+6,908)‎ . . N 2021 JMPSC Sprint Problems ‎ (Created page with "#This is a twenty question free-response test. Each question has exactly one integer answer. #You have 50 minutes to complete the test. #You will receive 3 points for each cor...")
• 22:49, 10 July 2021 (diff | hist) . . (+225)‎ . . N 2021 JMPSC Sprint Problems/Problem 20 ‎ (Created page with "==Problem== For all integers <math>x</math> and <math>y</math>, define the operation <math>\Delta</math> as <cmath>x \Delta y = x^3+y^2+x+y.</cmath> Find <cmath>\sqrt{\dfrac{2...")
• 22:48, 10 July 2021 (diff | hist) . . (+389)‎ . . N 2021 JMPSC Sprint Problems/Problem 19 ‎ (Created page with "==Problem== As an April Fool’s prank, Sean hacks his teacher’s digital clock and switches each digit to a certain letter. Right now, the hacked clock displays <math>\textb...")
• 22:47, 10 July 2021 (diff | hist) . . (+383)‎ . . N 2021 JMPSC Sprint Problems/Problem 18 ‎ (Created page with "==Problem== On square <math>ABCD</math> with side length <math>28</math>, <math>M</math> is the midpoint of <math>\overline{CD}</math>. Let <math>E</math> be the foot of the a...")
• 22:47, 10 July 2021 (diff | hist) . . (+139)‎ . . N 2021 JMPSC Sprint Problems/Problem 17 ‎ (Created page with "==Problem== What is the smallest positive multiple of <math>1003</math> that has no zeros in its decimal representation? ==Solution== asdf")
• 22:46, 10 July 2021 (diff | hist) . . (0)‎ . . 2021 JMPSC Sprint Problems/Problem 16 ‎ (→‎Problem)
• 22:46, 10 July 2021 (diff | hist) . . (+1)‎ . . 2021 JMPSC Sprint Problems/Problem 16 ‎ (→‎Problem)
• 22:46, 10 July 2021 (diff | hist) . . (+267)‎ . . N 2021 JMPSC Sprint Problems/Problem 16 ‎ (Created page with "==Problem== <math>ABCD</math> is a concave quadrilateral with <math>AB = 12</math>, <math>BC = 16</math>, <math>AD = CD = 26</math>, and <math>\angle ABC=90^\circ</math>. Fin...")
• 22:45, 10 July 2021 (diff | hist) . . (0)‎ . . N File:Sprint16.jpg ‎ (current)
• 22:38, 10 July 2021 (diff | hist) . . (+87)‎ . . N 2021 JMPSC Sprint Problems/Problem 15 ‎ (Created page with "==Problem== Find the last two digits of <math>10^{10}-5^{10}.</math> ==Solution== asdf")
• 22:37, 10 July 2021 (diff | hist) . . (-4)‎ . . 2021 JMPSC Sprint Problems/Problem 14 ‎ (→‎Problem)
• 22:37, 10 July 2021 (diff | hist) . . (+667)‎ . . N 2021 JMPSC Sprint Problems/Problem 14 ‎ (Created page with "==Problem== Ari, Bryant, Chandler, and David each tell one truth and one lie. Ari: Bryant is the tallest among the four of us. Chandler is the shortest among the four of us...")
• 22:23, 10 July 2021 (diff | hist) . . (+311)‎ . . 2021 JMPSC Sprint Problems/Problem 13 ‎ (→‎Problem)
• 22:23, 10 July 2021 (diff | hist) . . (+59)‎ . . N 2021 JMPSC Sprint Problems/Problem 13 ‎ (Created page with "==Problem== <center> 200px </center>")
• 22:22, 10 July 2021 (diff | hist) . . (0)‎ . . N File:Sprint14.jpg ‎ (current)
• 22:21, 10 July 2021 (diff | hist) . . (+198)‎ . . N 2021 JMPSC Sprint Problems/Problem 12 ‎ (Created page with "==Problem== The solution to the equation <math>x \sqrt{x \sqrt{x}}=2^{63}</math> can be written as <math>2^m</math>, where <math>m</math> is a real number. What is <math>m</ma...")
• 22:21, 10 July 2021 (diff | hist) . . (+146)‎ . . N 2021 JMPSC Sprint Problems/Problem 11 ‎ (Created page with "==Problem== How many numbers are in the finite sequence of consecutive perfect squares <cmath>9, 16, 25, \ldots , 2500?</cmath> ==Solution== asdf")
• 22:16, 10 July 2021 (diff | hist) . . (+435)‎ . . N 2021 JMPSC Sprint Problems/Problem 10 ‎ (Created page with "==Problem== Serena gets a grade of <math>75\%</math> for her chapter test. She doesn't remember how many problems there were, but she remembers that there were at most <math>1...")
• 22:16, 10 July 2021 (diff | hist) . . (+242)‎ . . N 2021 JMPSC Sprint Problems/Problem 9 ‎ (Created page with "==Problem== A machine cuts a piece of metal at a constant rate. After leaving the machine alone for twenty minutes, the metal has been split into six pieces. How many more min...")
• 22:15, 10 July 2021 (diff | hist) . . (+121)‎ . . N 2021 JMPSC Sprint Problems/Problem 8 ‎ (Created page with "==Problem== How many positive two-digit numbers exist such that the product of its digits is not zero? ==Solution== asdf")
• 22:14, 10 July 2021 (diff | hist) . . (0)‎ . . 2021 JMPSC Sprint Problems/Problem 7 ‎
• 22:14, 10 July 2021 (diff | hist) . . (+419)‎ . . N 2021 JMPSC Sprint Problems/Problem 7 ‎ (Created page with "==Problem== How many sets of three circles are in the diagram below such that their centers lie on the same line and each circle in the set is adjacent to another circle in th...")

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