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Values of a1- a2 + a3 - ... - a20 - Iran First Round 2018, P15

Source: Iran First Round 2017, P15

March 7, 2021
number theorycombinatorics

Problem Statement

Let a1,a2,a3,…,a20a_1, a_2, a_3, \dots, a_{20} be a permutation of the numbers 1,2,…,201, 2, \dots, 20. How many different values can the expression a1−a2+a3−⋯−a20a_1-a_2+a_3-\dots - a_{20} have?
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