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The original DOOM and DOOM 2 had a Nightmare difficulty mode, rumored to have been added by John Romero as a gimmick in a later version of the games, and in response to gamers at the time who found the games "too easy" and would send mail to id Software taunting them about it.
Selecting this difficulty warns players that "it's not an even remotely fair challenge". Every enemy in the game will immediately start shooting at you on sight, which makes hitscan enemies incredibly threatening. Enemy projectiles will travel at much faster speeds, which will keep you constantly dodging. And to make matters worse, enemies will respawn after a randomized time delay (the only exceptions are those which don't leave a corpse, like the Pain Elemental or Lost Souls). The only help the player gets is double ammo pickups, which reinforces the theory that this difficulty mode was added as an afterthought and with little care for balance.
Despite everything, there have been many players over the decades who have managed to beat all the levels in Nightmare mode with careful planning and lots of time and patience.