Given 100 chairs, keep one and skip the next. Repeat till only one chair remains.

seats.js

var Seat = function(number) {
	this.occupied = true;
	this.number = number;
}

var seats = [];

(function setup() {
	for (var i=0; i < 100; i++) {
		seats[i] = new Seat(i+1);
	}
})();

// Including the starting seat (start), what is the next occupied seat?
function findNextOccupiedSeat(seats, start) {

	if (start >= seats.length) {
		start = 0;
	}

	if (seats[start].occupied == true) {
		return start;
	}

	var found = false;
	var currSeat = start + 1;
	while (!found && currSeat !=start) {
		if (currSeat >= seats.length) {
			currSeat = 0;
		}

		if (seats[currSeat].occupied) {
			found = true;
		} else {
			currSeat++;
		}
	}

	return currSeat;
}

// Given a seat, dismiss it if it is not the last occupied seat
function dismissSeat(seats, seatNumber) {

	// find next occupied seat
	var nextOccSeat = findNextOccupiedSeat(seats, seatNumber + 1);

	// if it's not the same as current seat, then dismiss current seat
	if (seatNumber != nextOccSeat) {
		console.log('dismissing seat ' + seatNumber);
		seats[seatNumber].occupied = false;		
	} else {  // final answer
		return seatNumber;
	}

	// continue the search, skipping past that next occupied seat we found
	nextOccSeat++;
	if (nextOccSeat >= seats.length) {
		nextOccSeat = 0;
	}

	return dismissSeat(seats, findNextOccupiedSeat(seats, nextOccSeat));
}

var lastSeat = dismissSeat(seats, 0);
console.log('Last seat is ' + seats[lastSeat].number);