N=2^{12}=4096N=2 12 =4096 ways How to review the solution in polya strategy

In how many ways can you answer a 12-question true-false test if you answer each question with either a “true” or a “false”?

Solution

Step 1: Understand the problem.

Step 2: Devise a plan (translate).

Step 3: Carry out the plan (solve).

Step 4: Look back (check and interpret).

Step 1:Since there are 12 questions, and each question can be answered in 2 ways then:

1st question can be answered in 2 ways.

2nd question can be answered in 2 ways.

Step 2: The two questions can be answered in $2\times2=2^2$ ways.

The three questions can be answered in $2\times2\times 2=2^3$ ways. and so on.

Step 3: So we have:

$N=2^{12}=4096$

Step 4: There are 4096 ways to answer a 12-question true-false test if you answer each question with either a “true” or a “false”.

Therefore we have to prepare before the test to obtain the good score.