16.2.1. Counting Bad Strings

Try these first

1. 1.

   What is a bad binary string?

   Hint

   Think about the definition of bad strings.

2. 2.

   How many binary strings are there of length 1?

   Hint

   Count the combinations.

3. 3.

   What defines a bad string?

   • Contains '000'
   • Starts with 1
   • Ends with 0

   Hint

   Consider the definition.

4. 4.

   Is g(n) defined as the count of good strings?

   • True
   • False

   Hint

   Recall the definitions.

5. 5.

   Prove that f(n) is equal to 2^n - g(n) for n > 2.

   Hint

   Start with base cases like n=3 and n=4.

6. 6.

   Calculate the number of bad strings for n=5.

   Hint

   Remember to sum prior g(n) values and recalculate 2^5.