a) There is an unlimited set of cards with the words “abc”, “bca”, “cab” written. Of these, the word written is determined according to this rule. For the initial word, any card can be selected, and then on each turn to the existing word, you can either add on a card to the left or to the right, or cut the word anywhere (between the letters) and put a card there. Is it possible to make a palindrome with this method?
b) There is an unlimited set of red cards with the words “abc”, “bca”, “cab” and blue cards with the words “cba”, “acb”, “bac”. Using them, according to the same rules, a palindrome was made. Is it true that the same number of red and blue cards were used?
There are three piles of rocks: in the first pile there are 10 rocks, 15 in the second pile and 20 in the third pile. In this game (with two players), in one turn a player is allowed to divide one of the piles into two smaller piles. The loser is the one who cannot make a move. Which player would be the winner?