Xiao Ming goes to the theater to watch the performance. Count him from front to back in row 16 and from back to front in row 18. How many rows of seats are there in this theater?

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Let's solve this theater seating problem. Xiao Ming is sitting in a theater. When counting from the front to the back, he is in row 16. When counting from the back to the front, he is in row 18. We need to find the total number of rows in the theater. To understand this problem, we need to realize that Xiao Ming's row is being counted from both directions. When we count from the front, he is in position 16. When we count from the back, he is in position 18. The key insight is that his row appears in both counts, so we need to be careful not to double-count it. Now let's solve this step by step. The formula is: Total rows equals position from front plus position from back minus one. We subtract one because Xiao Ming's row is counted in both directions. So we have 16 plus 18 minus 1, which equals 34 minus 1, which equals 33 rows total. Let's verify our answer of 33 rows. From the front, Xiao Ming is indeed in row 16. From the back, we can check: if there are 33 rows total, then row 16 would be the 18th from the back, calculated as 33 minus 16 plus 1 equals 18. Both conditions are satisfied, confirming our answer is correct. To summarize what we've learned: When solving problems involving counting from both directions, we must be careful not to double-count the item in question. The formula is total equals front position plus back position minus one. In this case, the theater has 33 rows total.