Определите номер человека

import itertools
 
def cnt():
    i = 1
    while True:
        yield i
        if i == 19: i = 1
        else: i += 1
 
tmp = []
counter = cnt()
for item in itertools.cycle(range(1, 101)):
    if item not in tmp:
        i = next(counter)
        if i == 19:
            tmp.append(item)
            if len(tmp) == 100:
                print(item)
                break

s=18
a = [n for n in range(1, 101)]
 
while len(a) > 1:
    a.pop(s)
    s = (s + 18) % len(a)
print(*a)

class MyCircle:
    def __init__(self, n):
        self.hh = range(n)
        self.here = [True] * n
        self.n = n
 
    def __iter__(self):
        return Iterator(self)
 
class Iterator:
    def __init__(self, circle):
        self.circle = circle
        self.pos = -1
        self.step = 19
        self.total_cnt = 0
 
    def next(self):
        counter = 0
        while counter < self.step:
            self.pos = (self.pos + 1) % self.circle.n
            while not self.circle.here[self.pos]:
                self.pos = (self.pos + 1) % self.circle.n
            counter += 1
        number = self.circle.hh[self.pos]
        self.circle.here[self.pos] = False
        if self.total_cnt == self.circle.n:
            raise StopIteration()
        else:
            self.total_cnt += 1
            return number+1

circle = MyCircle(100)
for n in circle:
    print n

# -*- coding: utf-8 -*-
 
group = list(range(1, 101))
while len(group) > 1:
    del group[::18]
print(group)