Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "1996 AIME Problems"

(→‎Problem 2)
(→‎Problem 3)
Line 9: Line 9:
  
 
== Problem 3 ==
 
== Problem 3 ==
 +
Find the smallest positive integer <math>n</math> for which the expansion of <math>(xy-3x+7y-21)^n</math>, after like terms have been collected, has at least 1996 terms.
  
 
[[1996 AIME Problems/Problem 3|Solution]]
 
[[1996 AIME Problems/Problem 3|Solution]]

Revision as of 15:02, 24 September 2007

Problem 1

Solution

Problem 2

For each real number $x$, let $\lfloor x \rfloor$ denote the greatest integer that does not exceed x. For how man positive integers $n$ is it true that $n<1000$ and that $\lfloor \log_{2} n \rfloor$ is a positive even integer?

Solution

Problem 3

Find the smallest positive integer $n$ for which the expansion of $(xy-3x+7y-21)^n$, after like terms have been collected, has at least 1996 terms.

Solution

Problem 4

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

A $150\times 324\times 375$ rectangular solid is made by gluing together $1\times 1\times 1$ cubes. An internal diagonal of this solid passes through the interiors of how many of the $1\times 1\times 1$ cubes?

Solution

Problem 15

Solution

See also

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1996_AIME_Problems&oldid=16688"