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?
I got 497 am I correct?
To determine the numeral of the last person who remained in the circle, let's break down the process step-by-step.
First, let's consider the pattern of people staying or leaving the circle based on their numerals:
1st person: Jennifer Lopez look alike - says "one in" and remains in the circle.
2nd person: Basketball player - says "two out" and leaves the circle.
3rd person: Rap singer - says "three in" and remains in the circle.
4th person: US senator - says "four out" and leaves the circle.
From this pattern, we can observe that people wearing odd numerals stay in the circle, while people wearing even numerals leave the circle.
The count-off continues, with each subsequent person stating either "in" or "out" based on their numeral. The sequence of staying or leaving the circle follows the pattern: in, out, in, out, in, out, and so on.
Since there are 1000 people standing in the circle, this pattern will continue until only one person remains.
To find the final numeral, we need to count how many times this pattern repeats before reaching the Jennifer Lopez look alike again.
The pattern repeats every (in + out) = (1 + 2) = 3 people. So, after every three people, the Jennifer Lopez look alike will appear again.
Since the total number of people is 1000, we need to divide this by the pattern repetition count of 3 to determine the number of times the pattern repeats:
1000 / 3 = 333 repetitions with a remainder of 1.
This means the pattern repeats 333 times completely, and we are left with one person remaining after the 333rd repetition.
Now, we need to figure out which numeral this person has. Since the last person before the Jennifer Lopez look alike said "one thousand out" and left the circle, we know that the Jennifer Lopez look alike will say "one in."
Since the pattern follows an odd numeral for staying in the circle, the Jennifer Lopez look alike will have an odd numeral. Therefore, the last person remaining in the circle will have the numeral that comes right before the Jennifer Lopez look alike's numeral, which is one less than her numeral.
So, the numeral of the last person remaining in the circle is 333 repetitions before the Jennifer Lopez look alike's numeral, which is numerically one less than hers.
If Jennifer Lopez look alike's numeral is 1000, then the last person's numeral would be 1000 - 1 = 999.
Therefore, the numeral of the last person who remained in the circle is 999, not 497.