Once in a restaurant [b][i]Dr. Strange[/i][/b] found out that there were 12 types of food items from 1 to 12 on the menu. He decided to visit the restaurant 12 days in a row and try a different food everyday. 1st day, he tries one of the items from the first two. On the 2nd day, he eats either item 3 or the item he didn’t tried on the 1st day. Similarly, on the 3rd day, he eats either item 4 or the item he didn’t tried on the 2nd day. If someday he's not able to choose items that way, he eats the item that remained uneaten from the menu. In how many ways can he eat the items for 12 days?
1. **Understanding the Problem:**
   Dr. Strange has 12 types of food items numbered from 1 to 12. He visits the restaurant for 12 consecutive days and tries a different food item each day. The selection process is as follows:
   - On the 1st day, he tries one of the items from the first two (1 or 2).
   - On the 2nd day, he eats either item 3 or the item he didn’t try on the 1st day.
   - On the 3rd day, he eats either item 4 or the item he didn’t try on the 2nd day.
   - This pattern continues until the 12th day.
   - If someday he's not able to choose items that way, he eats the item that remained uneaten from the menu.

2. **Analyzing the Pattern:**
   - On the 1st day, he has 2 choices: item 1 or item 2.
   - On the 2nd day, he has 2 choices: item 3 or the item he didn’t try on the 1st day.
   - On the 3rd day, he has 2 choices: item 4 or the item he didn’t try on the 2nd day.
   - This pattern continues until the 12th day.

3. **Counting the

The final answer is \(\boxed{2048}\).