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sum of almost all r -tuples with components 1 or -1

Source: Spanish Mathematical Olympiad 1976 P2

December 23, 2022

vectorSumalgebra

Problem Statement

Consider the set

C

of all

r

-tuple whose components are

1

-1

. Calculate the sum of all the components of all the elements of

C

excluding the

r

-tuple

(1, 1, 1, . . . , 1)