2018 AIME I Problems
| 2018 AIME I (Answer Key) | AoPS Contest Collections • PDF | ||
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Instructions
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to 
, inclusive. Your score will be the number of correct answers; i.e., there is neither partial credit nor a penalty for wrong answers.Contents
Problem 1
Let 
be the number of ordered pairs of integers 
with 
and 
such that the polynomial 
can be factored into the product of two (not necessarily distinct) linear factors with integer coefficients. Find the remainder when is divided by 
.
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Find the number of four-element subsets of 
with the property that two distinct elements of a subset have a sum of 
, and two distinct elements of a subset have a sum of 
. For example, 
and 
are two such subsets.
Problem 10
The wheel shown below consists of two circles and five spokes, with a label at each point where a spoke meets a circle. A bug walks along the wheel, starting at point \(A\). At every step of the process, the bug walks from one labeled point to an adjacent labeled point. Along the inner circle the bug only walks in a circular clockwise direction, and along the outer circle the bug only walks in a clockwise direction. For example, the bug could travel along the path \(AJABCHCHIJA\), which has \(10\) steps. Let \(n\) be the number of paths with \(15\) steps that begin and end at point \(A\). Find the remainder when \(n\) is divided by \(1000\).
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
| 2018 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by 2017 AIME II |
Followed by 2018 AIME II | |
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| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
