TOT 029 1982 Autumn S3 60 symbols, either X or O on paper
Source:
August 18, 2019
combinatoricsWordsgame strategygame
Problem Statement
symbols, each of which is either or , are written consecutively on a strip of paper. This strip must then be cut into pieces with each piece containing symbols symmetric about their centre, e.g. , etc.
(a) Prove that there is a way of cutting the strip so that there are no more than such pieces.
(b) Give an example of such an arrangement of the signs for which the number of pieces cannot be less than .
(c) Try to improve the result of (b).