Factor cards is a one - player game using numbered cards. To begin with, all cards are in a central pile with their numbers visible. At each turn , exactly one card is moved from the central pile to the score pile and one or more cards are moved from central pile to the discard pile according to these rules.
Rule 1: A card may be moved to the score pile only if the number on the card has at least one of its factors, other than itself, still on the central pile.
Rule 2: When a card is moved to the score pile, all the cards that have factors of its number and are still in the central pile are moved to the discard pile.
Play stops when no card in the control pile has a factor other than itself in the central pile. The players score is the sum of all numbers on the cards in the score pile at the end of play.
In the following questions, the game starts with 20 cards numbered 1 to 20 and are therefore called 20-games.
A) Show steps that will produce a score of more than 100 points in a 20- game
B) What is the maximum score for a 20- game. Explain why it is the maximum
C) Explain why every 20- game ends with 8 or fewer cards in the score pile .