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ASU 210 All Soviet Union MO 1975 2^n digit number with only 1,2 differ

Source:

July 5, 2019

number theorycombinatoricsDigits

Problem Statement

Prove that it is possible to find

2^{n+1}

2^n

digit numbers containing only "

1

" and "

2

" as digits, such that every two of them distinguish at least in

2^{n-1}

digits.