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2000 AIME Problems
12
Different Values of Function
Different Values of Function
Source:
January 5, 2007
function
algorithm
Problem Statement
Given a function
f
f
f
for which
f
(
x
)
=
f
(
398
−
x
)
=
f
(
2158
−
x
)
=
f
(
3214
−
x
)
f(x)=f(398-x)=f(2158-x)=f(3214-x)
f
(
x
)
=
f
(
398
−
x
)
=
f
(
2158
−
x
)
=
f
(
3214
−
x
)
holds for all real
x
,
x,
x
,
what is the largest number of different values that can appear in the list
f
(
0
)
,
f
(
1
)
,
f
(
2
)
,
…
,
f
(
999
)
?
f(0),f(1),f(2),\ldots,f(999)?
f
(
0
)
,
f
(
1
)
,
f
(
2
)
,
…
,
f
(
999
)?
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