A domino is a rectangle formed by two congruent squares. Each square contains an orderly pattern of "pips" or dots representing a number from zero through six. Explore and develop methods and strategies to solve the following problems involving dominoes.
Problem 1:
How many different dominoes can be made with the above constraints or description of a domino? Make a list of the dominoes.
Problem 2:
Suppose four people are going to play a game of dominoes. Under the set of rules given to them, the first step is to divide the full set of dominoes equally among the four players. How many different ways can this division of the dominoes be made?
Problem 3:
After the dominoes are divided among the four players, the task of the game is to take turns and play the complete set of dominoes end to end to form a row. The one restriction is that the touching ends must have the same numerical value. How many different ways can a set of dominoes be arranged under this restriction? (Hint: How many different games can occur?)