Agent Argent's mission to penetrate the evil doctor's inner circle of J-men and thwart their plan to flood the Flooble-plex with substandard puzzles had reached an impasse. He had succesfully reached the evil doctor's outer court (in disguise) but now he was compromised.
As he was still breathing, he deduced that his nemesis knew only that he was in the room and did not know exactly who he was.
"The exits have been sealed," continued the voice, "my minions even now are lining up at the one door that can still be opened. They will each type a number into the keypad. If it is correct the door will open and they will come join me. If it is wrong they will fall through a trapdoor into the dungeon where they will suffer a horrible death exposed to a never-ending barrage of lateral thinking problems. Each number is different but my minions know the sequence. You do not, so, now I get to watch you squirm. HA HA HA HA HA HA HA HA ........."
Our hero got into the queue and waited. He was too far back to see what the first two villians typed. The first number he was able to glimpse was 22; the next villian typed 5. These were followed by three more of Levik's minions who typed 23, 7 and 222 respectively. Then it was his turn.
What number did Agent Argent type? and what happened? Remember, he is no fool, after all he is the holder of a nonhereditary dignity conferred by a sovereign.
Solution
