User contributions
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- 16:16, 1 April 2021 (diff | hist) . . (+1,108) . . N 2021 JMC 10 Problems/Problem 13 (Created page with "==Problem== An angle chosen from <math>1^{\circ},2^{\circ}, \dots,90^{\circ}</math> and an angle chosen from <math>1^{\circ},2^{\circ},\dots,89^{\circ}</math> determine two a...")
- 16:15, 1 April 2021 (diff | hist) . . (+1,080) . . N 2021 JMC 10 Problems/Problem 12 (Created page with "==Problem== Mihir draws line <math>y=2x</math> and Nathan draws line <math>x+y = n</math> for an integer <math>n.</math> The two lines divide the region <math>y \ge x^2</math...") (current)
- 16:14, 1 April 2021 (diff | hist) . . (+2) . . 2021 JMC 10 Problems/Problem 11 (→Solution) (current)
- 16:14, 1 April 2021 (diff | hist) . . (+736) . . N 2021 JMC 10 Problems/Problem 11 (Created page with "==Problem== There exist positive integers <math>k</math> that satisfy <math>k = 3\gcd(20,k).</math> What is the sum of all possible values of <math>k?</math> <math>\textbf{(...")
- 16:13, 1 April 2021 (diff | hist) . . (+928) . . N 2021 JMC 10 Problems/Problem 10 (Created page with "==Problem== Let <math>ABCD</math> be a square with sides of length <math>4.</math> Point <math>X</math> is on side <math>{CD}</math> and point <math>Y</math> is on side <math...") (current)
- 16:12, 1 April 2021 (diff | hist) . . (+598) . . N 2021 JMC 10 Problems/Problem 9 (Created page with "==Problem== In Malachar, the number system is identical to ours, but all real numbers are written with digits in reverse order. A citizen in Malachar writes <math>15\cdot 73....") (current)
- 16:11, 1 April 2021 (diff | hist) . . (+952) . . N 2021 JMC 10 Problems/Problem 8 (Created page with "==Problem== A positive integer is ''pretentious'' if it has both even and odd digits. For example, <math>74</math> and <math>83</math> are pretentious. How many pretentious t...") (current)
- 16:10, 1 April 2021 (diff | hist) . . (+793) . . N 2021 JMC 10 Problems/Problem 7 (Created page with "==Problem== For some real <math>x,</math> the area of a square equals <math>3x+1</math> and the product of the lengths of its diagonals equals <math>5x+7.</math> What is the...") (current)
- 16:09, 1 April 2021 (diff | hist) . . (+568) . . N 2021 JMC 10 Problems/Problem 6 (Created page with "==Problem 6== The sum of the ages of a family equals <math>78.</math> Fifteen years later, the sum of their ages is equal to <math>153.</math> How many people are in this fami...") (current)
- 16:08, 1 April 2021 (diff | hist) . . (+677) . . N 2021 JMC 10 Problems/Problem 5 (Created page with "==Problem== A mixture has <math>96</math> grams of aluminum and <math>4</math> grams of barium. Nir the chemist uses magic to remove some aluminum. Now, exactly <math>90\%</ma...") (current)
- 16:07, 1 April 2021 (diff | hist) . . (+782) . . N 2021 JMC 10 Problems/Problem 4 (Created page with "==Problem== A day in the format <math>mm/dd</math> is called ''binary'' if all of the digits are either <math>0</math>s or <math>1</math>s with leading zeros allowed. How many...") (current)
- 16:06, 1 April 2021 (diff | hist) . . (+875) . . N 2021 JMC 10 Problems/Problem 3 (Created page with "==Problem== A group of <math>8</math> people are either honest or liars, where honest people always tell the truth and liars always lie. People <math>P_1,P_2, \cdots, P_8</mat...") (current)
- 16:05, 1 April 2021 (diff | hist) . . (+927) . . N 2021 JMC 10 Problems/Problem 18 (Created page with "==Problem 18== If <math>x,y,</math> and <math>z</math> are positive real numbers that satisfy the equation <cmath>xy+yz+xz=96(y+z)-x^2 = 24(x+z) -y^2 = 54(x+y) -z^2,</cmath>...") (current)
- 16:03, 1 April 2021 (diff | hist) . . (-2) . . 2021 JMC 10 Problems/Problem 19 (→Solution) (current)
- 16:02, 1 April 2021 (diff | hist) . . (+1,172) . . N 2021 JMC 10 Problems/Problem 19 (Created page with "==Problem== Two distinct divisors of <math>6^4=1296</math> are ''mutual'' if their difference divides their product. For instance, <math>(4,2)</math> is mutual as <math>(4-2)...")
- 16:00, 1 April 2021 (diff | hist) . . (+4,160) . . N 2021 JMC 10 Problems/Problem 20 (Created page with "==Problem== A particle is in a <math>5 \times 5</math> grid. Each second, it moves to an adjacent cell and when traveling from a cell to another cell, it takes one of the pat...")
- 15:56, 1 April 2021 (diff | hist) . . (-13) . . 2021 JMC 10 Problems/Problem 21 (→Solution) (current)
- 15:55, 1 April 2021 (diff | hist) . . (+2,432) . . N 2021 JMC 10 Problems/Problem 21 (Created page with "==Problem== Two identical circles <math>\omega_{a}</math> and <math>\omega_{b}</math> with radius <math>1</math> have centers that are <math>\tfrac{4}{3}</math> units apart. T...")
- 15:51, 1 April 2021 (diff | hist) . . (+1,119) . . N 2021 JMC 10 Problems/Problem 22 (Created page with "==Problem== Let <math>r_1,r_2,r_3,r_4</math> be the roots of <math>P(x)= x^4+4x^3-3x^2+2x-1.</math> Suppose <math>Q(x)</math> is the monic polynomial with all six roots in th...") (current)
- 15:49, 1 April 2021 (diff | hist) . . (+1,733) . . N 2021 JMC 10 Problems/Problem 23 (Created page with "==Problem== An invisible ant and an anteater, at the same constant speed of <math>1</math> edge length per second, start at (not necessarily distinct) randomly chosen vertice...") (current)
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