start checking after each round
after round 1, 500 people remain, numbered 2k+1
after round 2, 250 remain, numbered 4k+1
after round 3, 125 remain, numbered 8k+1
at this point, #1 still remains, but starting with the next cycle, 16k+1, overlap starts to set in
1,17,33,...,993
Now #1 has to leave, so the people left standing are of the form
17,49,81,... 32k-15 ..., 977
There are only a few cycles left, and I'm sure you can sort them out.
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?
2 answers
Is it 497?
2 answers