Stierlitz encrypts a 100-digit binary string
Source: St Petersburg 2021 10.4
December 23, 2021
combinatorics
Problem Statement
Stierlitz wants to send an encryption to the Center, which is a code containing characters, each a "dot" or a "dash". The instruction he received from the Center the day before about conspiracy reads: i) when transmitting encryption over the radio, exactly characters should be replaced with their opposites;ii) the location of the "wrong" characters is decided by the transmitting side and the Center is not informed of it.Prove that Stierlitz can send encryptions, each time choosing some characters to flip, such that when the Center receives these ciphers, it may unambiguously restore the original code.