One thousand people stood in a very large circle. Each starting with the Jennifer Lopez look alike, wore a sign on his or her back with a numeral from 1 to 1000 in a clockwise sequence. They began counting off. The Jennifer Lopez look alike said one in and remained in the circle. The 7'6" basketball player to her left said two out and left circle. The rap singer next in sequence said said three in and remained in the circle. The United States senator who was next in the sequence said four out and left the circle.
So it continued with each person sporting an odd numeral and with every person wearing an even numeral leaving the circle.
It was easy to visualize who remained in the circle when the count off again reached the Jennifer Lopez look alike. Since the person before her said one thousand out and left the circle, she now said one in and stayed in the circle. Continuing this sequence the rap singer said three out and left the circle. This process would keep going on and in until only one person was left in the circle.
What was the numeral of the last person who remained in the circle?
http://www.jiskha.com/display.cgi?id=1470359781
497
To solve this problem, we need to carefully follow the pattern and count the remaining person in each round. Let's break it down step by step:
1. The Jennifer Lopez look alike starts and says "one in" and remains in the circle. So, 999 people are left in the circle.
2. The 7'6" basketball player says "two out" and leaves the circle. Now, 998 people are left in the circle.
3. The rap singer says "three in" and remains in the circle. So, 997 people are left in the circle.
4. The United States senator says "four out" and leaves the circle. Now, 996 people are left in the circle.
From this pattern, we can observe that in each round, the number of people remaining in the circle decreases by 1. Also, each person follows a precise pattern of saying either "in" or "out" based on their position in the counting sequence.
Continuing this process, we can calculate the final person remaining in the circle:
- The counting continues, alternating between "in" and "out" until the number sequence reaches 1,000.
- The Jennifer Lopez look alike, being the last person to say "in," remains in the circle.
- The person before Jennifer Lopez (numeral 999) says "one thousand out" and leaves the circle.
- The person after Jennifer Lopez (numeral 1) says "two in" and remains in the circle.
Thus, the last person who remains in the circle has the numeral 1.