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Sweden Contests
Swedish Mathematical Competition
1980 Swedish Mathematical Competition
2
2
Part of
1980 Swedish Mathematical Competition
Problems
(1)
|a_i - b_i| not all different, when a_i,b_i permutations of 1-7
Source: 1980 Swedish Mathematical Competition p2
3/28/2021
a
1
a_1
a
1
,
a
2
a_2
a
2
,
a
3
a_3
a
3
,
a
4
a_4
a
4
,
a
5
a_5
a
5
,
a
6
a_6
a
6
,
a
7
a_7
a
7
and
b
1
b_1
b
1
,
b
2
b_2
b
2
,
b
3
b_3
b
3
,
b
4
b_4
b
4
,
b
5
b_5
b
5
,
b
6
b_6
b
6
,
b
7
b_7
b
7
are two permutations of
1
,
2
,
3
,
4
,
5
,
6
,
7
1, 2, 3, 4, 5, 6, 7
1
,
2
,
3
,
4
,
5
,
6
,
7
. Show that
∣
a
1
−
b
1
∣
|a_1 - b_1|
∣
a
1
−
b
1
∣
,
∣
a
2
−
b
2
∣
|a_2 - b_2|
∣
a
2
−
b
2
∣
,
∣
a
3
−
b
3
∣
|a_3 - b_3|
∣
a
3
−
b
3
∣
,
∣
a
4
−
b
4
∣
|a_4 - b_4|
∣
a
4
−
b
4
∣
,
∣
a
5
−
b
5
∣
|a_5 - b_5|
∣
a
5
−
b
5
∣
,
∣
a
6
−
b
6
∣
|a_6 - b_6|
∣
a
6
−
b
6
∣
,
∣
a
7
−
b
7
∣
|a_7 - b_7|
∣
a
7
−
b
7
∣
are not all different.
combinatorics
permutation