60 symbols, each of which is either X or O, 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. O,XX,OXXXXX,XOX, etc.
(a) Prove that there is a way of cutting the strip so that there are no more than 24 such pieces.
(b) Give an example of such an arrangement of the signs for which the number of pieces cannot be less than 15.
(c) Try to improve the result of (b). combinatoricsWordsgame strategygame