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Kürschák Math Competition
1957 Kurschak Competition
3
3
Part of
1957 Kurschak Competition
Problems
(1)
max of |a_1 - 1| + |a_2-2|+...+ |a_n- n| where a_i is permutation of i
Source: 1957 Hungary - Kürschák Competition p3
10/10/2022
What is the largest possible value of
∣
a
1
−
1
∣
+
∣
a
2
−
2
∣
+
.
.
.
+
∣
a
n
−
n
∣
|a_1 - 1| + |a_2-2|+...+ |a_n- n|
∣
a
1
−
1∣
+
∣
a
2
−
2∣
+
...
+
∣
a
n
−
n
∣
where
a
1
,
a
2
,
.
.
.
,
a
n
a_1, a_2,..., a_n
a
1
,
a
2
,
...
,
a
n
is a permutation of
1
,
2
,
.
.
.
,
n
1,2,..., n
1
,
2
,
...
,
n
?
algebra
inequalities
permutation
combinatorics