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2018 AIME Problems
15
Inequality FE
Inequality FE
Source: 2018 AIME II #15
March 23, 2018
inequalities
Problem Statement
Find the number of functions
f
f
f
from
{
0
,
1
,
2
,
3
,
4
,
5
,
6
}
\{0,1,2,3,4,5,6\}
{
0
,
1
,
2
,
3
,
4
,
5
,
6
}
to the integers such that
f
(
0
)
=
0
,
f
(
6
)
=
12
f(0)=0, f(6)=12
f
(
0
)
=
0
,
f
(
6
)
=
12
, and
∣
x
−
y
∣
≤
∣
f
(
x
)
−
f
(
y
)
∣
≤
3
∣
x
−
y
∣
|x-y| \le |f(x)-f(y)| \le 3 |x-y|
∣
x
−
y
∣
≤
∣
f
(
x
)
−
f
(
y
)
∣
≤
3∣
x
−
y
∣
for all
x
x
x
and
y
y
y
in
{
0
,
1
,
2
,
3
,
4
,
5
,
6
}
\{0,1,2,3,4,5,6\}
{
0
,
1
,
2
,
3
,
4
,
5
,
6
}
.
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