Difference between revisions of "2020 AIME I Problems"
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==Problem 5== | ==Problem 5== | ||
− | + | Six cards numbered <math>1</math> through <math>6</math> are to be lined up in a row. Find the number of arrangements of these six cards where one of the cards can be removed leaving the remaining five cards in either ascending or descending order. | |
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[[2020 AIME I Problems/Problem 5 | Solution]] | [[2020 AIME I Problems/Problem 5 | Solution]] |
Revision as of 15:39, 12 March 2020
2020 AIME I (Answer Key) | AoPS Contest Collections • PDF | ||
Instructions
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Contents
[hide]Problem 1
In with point lies strictly between and on side and point lies strictly between and on side such that The degree measure of is where and are relatively prime positive integers. Find
Problem 2
There is a unique positive real number such that the three numbers and in that order, form a geometric progression with positive common ratio. The number can be written as where and are relatively prime positive integers. Find
Problem 3
A positive integer has base-eleven representation and base-eight representation where and represent (not necessarily distinct) digits. Find the least such expressed in base ten.
Problem 4
Let be the set of positive integers with the property that the last four digits of are and when the last four digits are removed, the result is a divisor of For example, is in because is a divisor of Find the sum of all the digits of all the numbers in For example, the number contributes to this total.
Problem 5
Six cards numbered through are to be lined up in a row. Find the number of arrangements of these six cards where one of the cards can be removed leaving the remaining five cards in either ascending or descending order.
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Let
2020 AIME I (Problems • Answer Key • Resources) | ||
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Followed by 2020 AIME II | |
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The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.