In De Ligt Hotel, Elliot did not head to the reception to ask about Hayden. Avery had done so, and if the receptionist said that there was no information, then it had to be true.
It was either that Hayden had come to Ylore with a forged identity, or he had checked out from the hotel as soon as he spotted Elliot.
Elliot had to find out if Hayden had indeed been to this hotel, and he went straight to the guard room. There he asked for this morning's surveillance footage.
"What does the person