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Iran MO (1st Round)
2018 Iran MO (1st Round)
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2018 Iran MO (1st Round)
Problems
(1)
Values of a1- a2 + a3 - ... - a20 - Iran First Round 2018, P15
Source: Iran First Round 2017, P15
3/7/2021
Let
a
1
,
a
2
,
a
3
,
…
,
a
20
a_1, a_2, a_3, \dots, a_{20}
a
1
,
a
2
,
a
3
,
…
,
a
20
be a permutation of the numbers
1
,
2
,
…
,
20
1, 2, \dots, 20
1
,
2
,
…
,
20
. How many different values can the expression
a
1
−
a
2
+
a
3
−
⋯
−
a
20
a_1-a_2+a_3-\dots - a_{20}
a
1
−
a
2
+
a
3
−
⋯
−
a
20
have?
number theory
combinatorics