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Korea Junior Mathematics Olympiad
2024 Korea Junior Math Olympiad (First Round)
19.
algebra finding maximum
algebra finding maximum
Source: 2024 KJMO first round
October 27, 2024
algebra
maximum value
Inequality
Problem Statement
For all integers
a
0
,
a
1
,
⋅
⋅
⋅
a
100
{a}_{0},{a}_{1}, \cdot\cdot\cdot {a}_{100}
a
0
,
a
1
,
⋅
⋅
⋅
a
100
, find the maximum of
a
5
−
2
a
40
+
3
a
60
−
4
a
95
{a}_{5}-2{a}_{40}+3{a}_{60}-4{a}_{95}
a
5
−
2
a
40
+
3
a
60
−
4
a
95
★
\bigstar
★
1)
a
0
=
a
100
=
0
{a}_{0}={a}_{100}=0
a
0
=
a
100
=
0
2) for all
i
=
0
,
1
,
⋅
⋅
⋅
99
,
i=0,1,\cdot \cdot \cdot 99,
i
=
0
,
1
,
⋅
⋅
⋅
99
,
∣
a
i
+
1
−
a
i
∣
≤
1
|{a}_{i+1}-{a}_{i}|\le1
∣
a
i
+
1
−
a
i
∣
≤
1
3)
a
10
=
a
90
{a}_{10}={a}_{90}
a
10
=
a
90
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