Does Mr. X reveal his location on every turn of the travel log that is circled?

Mr X. reveals his current location on, and only on, the circled turns, or at any time he is on the same space as a police player (in which case he immediately loses the game and the police players win the game). All remaining turns (the majority) are played as hidden information.

Keep in mind that if Mr. X uses a Double Move Token to skip over a reveal turn, Mr. X must still reveal where he was at that time even though he is no longer there. For this reason as well as convenience, it is a common house rule to leave the Mr. X token on his "last known location" at the last time of reveal.