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default / train
(m)/(n) is the Irreducible fraction value of 3+(1)/(3+(1)/(3+(1)/(3))), what is the value of m+n?
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_1
task_id
481db7b0-a28e-5d43-85d0-ce43c4514b39
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f1
default / train
What is the value of (log5)³+(log20)³+(log8)(log0.25) where log denotes the base-ten logarithm?
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_14
task_id
62fbc1be-7aee-50ad-895e-29567c217a13
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f14
default / train
The roots of the polynomial 10x³−39x²+29x−6 are the height, length, and width of a rectangular box (right rectangular prism). A new rectangular box is formed by lengthening each ed…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_15
task_id
1d26a182-9917-55eb-8c64-bcb2cce28ad3
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f15
default / train
Suppose a is a real number such that the equation a⋅(sinx+sin(2x))=sin(3x) has more than one solution in the interval (0,π). The set of all such a that can be written in the form …
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_17
task_id
645533d4-4b22-59ca-8ebe-9259b727a057
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f17
default / train
Let T_(k) be the transformation of the coordinate plane that first rotates the plane k degrees counterclockwise around the origin and then reflects the plane across the y-axis. Wha…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_18
task_id
2c45ef9f-1174-5f97-b128-f6e15b8045a3
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f18
default / train
The sum of three numbers is 96. The first number is 6 times the third number, and the third number is 40 less than the second number. What is the absolute value of the difference b…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_2
task_id
38c81e42-ea96-52bb-8a3a-7b71ff6c5561
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f2
default / train
Let h_(n) and k_(n) be the unique relatively prime positive integers such that (1)/(1)+(1)/(2)+(1)/(3)+⋯+(1)/(n)=(h_(n))/(k_(n)). Let L_(n) denote the least common multiple of the …
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_23
task_id
85031697-9ecf-5312-ba59-8470c023517e
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f23
default / train
How many strings of length 5 formed from the digits 0, 1, 2, 3, 4 are there such that for each j∈{1,2,3,4}, at least j of the digits are less than j? (For example, 02214 satisfies …
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_24
task_id
584f1006-d654-5abc-8737-8a96c039f458
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f24
default / train
A circle with integer radius r is centered at (r,r). Distinct line segments of length c_(i) connect points (0,a_(i)) to (b_(i),0) for 1≤i≤14 and are tangent to the circle, where …
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_25
task_id
2d701f58-1285-5fdc-8958-607838ed0eb8
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f25
default / train
The textit{taxicab distance} between points (x₁,y₁) and (x₂,y₂) in the coordinate plane is given by |x₁−x₂|+|y₁−y₂|. For how many points P with integer coordinates is the taxicab d…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_5
task_id
6082ccfa-3e2c-5868-b8c1-8e2f3048d724
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f5
default / train
The infinite product
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_8
task_id
78a556ab-db18-5d20-ba62-2bd4a97a4e26
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f8
default / train
On Halloween 31 children walked into the principal's office asking for candy. They can be classified into three types: Some always lie; some always tell the truth; and some alterna…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_9
task_id
162e20f7-2bd0-50cc-91ce-7a87ea379ba2
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f9
default / train
Define xdiamond y to be |x−y| for all real numbers x and y. What is the value of ((1diamond2)diamond3)-(1diamond(2diamond3))?
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_1
task_id
68b1947e-81ec-5a64-8e9c-811851d17d45
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f1
default / train
Let f(n)=((−1+i√(3))/(2))^(n)+((−1−i√(3))/(2))^(n), where i=√(−1). What is f(2022)?
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_11
task_id
03ec4d4f-95d0-5a46-8c90-48f75c156a71
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f11
default / train
The diagram below shows a rectangle with side lengths 4 and 8 and a square with side length 5. Three vertices of the square lie on three different sides of the rectangle, as shown.…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_13
task_id
16020073-cb78-5cdc-92cb-a909a168c30d
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f13
default / train
The graph of y=x²+2x−15 intersects the x-axis at points A and C and the y-axis at point B. What is the numerator of the simplest fraction that represents tan(∠ABC)?
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_14
task_id
80a39553-9363-5723-9f08-cc3feed79c9f
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f14
default / train
In △ABC medians (AD)¯ and (BE)¯ intersect at G and △AGE is equilateral. Then cos(C) can be written as (m√(p))/(n), where m and n are relatively prime positive integers and p is a p…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_19
task_id
7785c1e0-ec5b-57cf-b369-f406ecb7ad80
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f19
default / train
In rhombus ABCD, point P lies on segment (AD)¯ so that (BP)¯ ⊥ (AD)¯, AP=3, and PD=2. What is the area of ABCD? (Note: The figure is not drawn to scale.)
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_2
task_id
49fb15ee-886a-50f4-b555-859c9040c9fe
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f2
default / train
Let S be the set of circles in the coordinate plane that are tangent to each of the three circles with equations x²+y²=4, x²+y²=64, and (x−5)²+y²=3. What is the sum of the areas of…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_21
task_id
587e62a8-8525-58e7-b9cd-13f811177364
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f21
default / train
Ant Amelia starts on the number line at 0 and crawls in the following manner. For n=1,2,3, Amelia chooses a time duration t_(n) and an increment x_(n) independently and uniformly a…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_22
task_id
8582f6f2-d602-5df6-bc9b-e02af6a16f44
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f22
default / train
Four regular hexagons surround a square with side length 1, each one sharing an…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_25
task_id
5b4bc190-f720-58b4-bc1d-a916f49de542
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f25
default / train
How many of the first ten numbers of the sequence 121,11211,1112111,… are prime numbers?
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_3
task_id
7c724347-0e9f-5193-a957-746048080c29
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f3
default / train
For how many values of the constant k will the polynomial x²+kx+36 have two distinct integer roots?
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_4
task_id
17794e6a-e761-5825-8b96-aac431bda0fa
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f4
default / train
What is the sum of the x and y coordinates of the new position of the point…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_5
task_id
861bca5f-7d80-57e7-b65f-c4a1659c0334
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f5
default / train
Camila writes down five positive integers. The unique mode of these integers is…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_7
task_id
1b60b0a0-6fee-53e0-a6da-e29157861e1f
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f7
default / train
Cities A and B are 45 miles apart. Alicia lives in A and Beth lives in B. Alicia bikes towards B at 18 miles per hour. Leaving at the same time, Beth bikes toward A at 12 miles per…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_1
task_id
48f94e01-6ea1-5b33-b7b1-818017a09f53
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f1
default / train
Positive real numbers x and y satisfy y³=x² and (y−x)²=4y². What is x+y?
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_10
task_id
145f2b26-57ba-5227-8d0e-5de8832d70ed
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f10
default / train
What is the degree measure of the acute angle formed by lines with slopes 2 and (1)/(3)?
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_11
task_id
7f3b1f80-ef36-504e-ae05-f4e4df0a0444
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f11
default / train
In a table tennis tournament every participant played every other participant…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_13
task_id
84a8ef78-a111-56d7-a905-4fed683f6bcc
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f13
default / train
Flora the frog starts at 0 on the number line and makes a sequence of jumps to…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_17
task_id
7165f327-8647-550a-a28a-90c2e4f4e770
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f17
default / train
What is the product of all solutions to the equation
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_19
task_id
223ff5f2-8306-5f7d-a47d-f67a721e11ca
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f19
default / train
The weight of (1)/(3) of a large pizza together with 3(1)/(2) cups of orange slices is the same as the weight of (3)/(4) of a large pizza together with (1)/(2) cup of orange slices…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_2
task_id
617fa2f8-5ebd-5add-a81c-6ad058e9065e
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f2
default / train
Rows 1, 2, 3, 4, and 5 of a triangular array of integers are shown below.
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_20
task_id
0cbfb0d2-0d66-5549-8658-7ef7a7ce50e3
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f20
default / train
If A and B are vertices of a polyhedron, define the distance d(A,B) to be the minimum number of edges of the polyhedron one must traverse in order to connect A and B. For example, …
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_21
task_id
7b7f2b63-b22f-54e1-b110-6c2e32f6d10b
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f21
default / train
How many ordered pairs of positive real numbers (a,b) satisfy the equation
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_23
task_id
1262875f-5d43-5f7f-9932-be130dfd0b35
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f23
default / train
Let K be the number of sequences A₁, A₂, …, A_(n) such that n is a positive integer less than or equal to 10, each A_(i) is a subset of {1,2,3,…,10}, and A_(i−1) is a subset of …
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_24
task_id
8512ebae-eaa5-500a-9acf-4c1477055457
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f24
default / train
There is a unique sequence of integers a₁,a₂,⋯a₂₀₂₃ such that
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_25
task_id
106053c5-e3ff-5636-94c4-8af2a68e3ed6
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f25
default / train
How many positive perfect squares less than 2023 are divisible by 5?
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_3
task_id
301a238a-a5d9-5dd3-8f19-3dece24a7f24
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f3
default / train
Points A and B lie on the graph of y=log₂x. The midpoint of (AB)¯ is (6,2). What is the positive difference between the x-coordinates of A and B? The final answer can be written in…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_6
task_id
1981fafe-2ed7-5ca2-a9ba-895e6bc04643
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f6
default / train
In the xy-plane, a circle of radius 4 with center on the positive x-axis is tangent to the y-axis at the origin, and a circle with radius 10 with center on the positive y-axis is t…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_10
task_id
802a3788-a630-5694-a905-927aac238a4e
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12B~5fProblems~2fProblem~5f10
default / train
Calculate the maximum area of an isosceles trapezoid that has legs of length 1 and one base twice as long as the other. The final answer can be written in the form (m)/(n), where m…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_11
task_id
7ef548b2-a990-5dd8-a89f-89d8df701a9a
task_key
default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12B~5fProblems~2fProblem~5f11
default / train
For how many ordered pairs (a,b) of integers does the polynomial x³+ax²+bx+6 have 3 distinct integer roots?
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_14
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Triangle ABC has side lengths in arithmetic progression, and the smallest side has length 6. If the triangle has an angle of 120^(∘), Find the area of ABC. The final answer can be …
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_17
task_id
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Carlos went to a sports store to buy running shoes. Running shoes were on sale,…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_2
task_id
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When n standard six-sided dice are rolled, the product of the numbers rolled can be any of 936 possible values. What is n?
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_23
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Suppose that a, b, c and d are positive integers satisfying all of the following relations. abcd=2⁶⋅3⁹⋅5⁷ lcm(a,b)=2³⋅3²⋅5³ lcm(a,c)=2³⋅3³⋅5³ lcm(a,d)=2³⋅3³⋅5³ lcm(b,c)=2¹⋅3³⋅5² …
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_24
task_id
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You are playing a game. A 2×1 rectangle covers two adjacent squares (oriented either horizontally or vertically) of a 3×3 grid of squares, but you are not told which two squares ar…
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_5
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For how many integers n does the expression√((log(n²)−(logn)²)/(logn−3))represent a real number, where log denotes the base 10 logarithm?
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_7
task_id
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How many nonempty subsets B of 0,1,2,3,⋯,12 have the property that the number of elements in B is equal to the least element of B? For example, B=4,6,8,11 satisfies the condition.
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_8
task_id
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What is the area of the region in the coordinate plane defined by
Answer published by the source
Identifiers
upstream_id
https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_9
task_id
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task_key
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