PROBLEM 1 Polya's four -step plan involves the following steps : 1. Understand the problem 2. Devise a plan 3. Carry out the plan 4. Look back Problem 1. In a class experiment, Miguel rolls one ordinary 6-sided die repeatedly. Keeping track of each number he rolls, he decides to stop as soon as one number is rolled three times. Miguel stops after the 12th roll, and the sum of these rolls is 47. Which number occurred for the third time ? (An ordinary 6-sided die has the numbers from 1 through 6 on its sides ) Answer : 1. Understand the problem > Miguel will stop rolling dice when one number is repeated three times . On the 12th roll , Miguel stops , and the sum of these rolls is 47 . > This shows that he tried twelve times to get one number that was repeated three times We are to determine which number(n= 1,2,3,4,5,6) occurred for the third time? 2. Devise a plan We choose a strategy of logical reasoning because it is the process of deriving a logical inference from a hypothesis through reasoning . This generates reason for our own point that we can predict the next number given by the situation . (Logical inference- The act or process of deriving logical conclusions from premises known or assumed to be true). 3. Carry out the plan On the 11th roll , no number still appeared to be repeated three times This means that five of the numbers appeared twice, and the one in the number there appeared only once