Did one of the racers specifically say that anyone with any flying skill was barred? You know, that's really evil of you, since there's no way to untrain skills, so for all you know, we might have all our duck slots filled with ducks who can fly.
Oh wait, apparently that is how they translate into numbers, but it won't tell you if you get the combo correct before pulling the lever (which you need another tool to fix before you can pull it).
So apparently the combo is 1 3 2 3, but how exactly do the blocks above the buttons translate into numbers? It doesn't seem to be the number of pairs of triangles that you can see below the leaves.
The game is really easy, but this is one of those games with a purpose other than testing the player's skill. To truly appreciate it, you have to read the story that comes with it.
I can confirm Ampryx's comment about upgrading armour. I actually upgraded my armour when I was down to 1 HP in one run, then suddenly BAM! Full health!
 "Rebuild 2"){kind=icon}
 "Tower of Greed"){kind=icon}
 "DuckLife 4"){kind=icon}
 "Nelly"){kind=icon}
 "The Fabulous Screech"){kind=icon}
 "Sushi Cat 2"){kind=icon}
 "This is the Only Level 3"){kind=icon}
 "ClickRace"){kind=icon}
 "Cuboy: Cubeture 2"){kind=icon}
 "Hell Tetris"){kind=icon}
 "Momentum Missile Mayhem 2"){kind=icon}
 "Musaic Box"){kind=icon}
 "Medieval Character Maker"){kind=icon}
 "Ultimate Santa Battle"){kind=icon}
 "Missilebreak Outvaders"){kind=icon}
 "Bloons Tower Defense 4"){kind=icon}
 "Trigger Knight"){kind=icon}