MathDB

Multiply by the next one - 2^k-tuples

Source: 1961 All-Soviet Union Olympiad

August 4, 2015

combinatoricsinvarianttransformation

Problem Statement

Consider a

2^k

-tuple of numbers

(a_1,a_2,\dots,a_{2^k})

all equal to

1

or

-1

. In one step, we transform it to

(a_1a_2,a_2a_3,\dots,a_{2^k}a_1)

. Prove that eventually, we will obtain a

2^k

-tuple consisting only of

1

's.

Back to Problems View on AoPS