1984 AIME Problems
Contents
Problem 1
Find the value of if
,
,
is an arithmetic progression with common difference 1, and
.
Problem 2
The integer is the smallest positive multiple of
such that every digit of
is either
or
. Compute
.
Problem 3
A point is chosen in the interior of
such that when lines are drawn through
parallel to the sides of
, the resulting smaller triangles
,
, and
in the figure, have areas
,
, and
, respectively. Find the area of
.
Problem 4
Let be a list of positive integers - not necessarily distinct - in which the number
appears. The arithmetic mean of the numbers in
is
. However, if
is removed, the arithmetic mean of the numbers is
. What's the largest number that can appear in
?