Take, for instance, Gordon Murray's outstandingly brilliant cheat for the 1981 season with the Brabham BT49C. The wonderful documentary How To Go Fast And Influence People explains that the rules required that all cars must have a minimum ride height of 6cm. Gordon figured that the only way to measure this height was when the car was stationary, in the pits. Therefore, if he could figure out a way that the car could be lower than 6cm on the track and then return to 6cm in the pits,t he car would be legal.
He did it. He linked the suspension to a hydraulic reservoir with a pinhole exit. When the car was at speed, the pressure on the car was strong enough to press it low to the ground, and the pinhole exit was small enough that air couldn't leak out. That meant the hydraulic fluid kept the car low.
When the car came to a stop, there was no more pressure pushing the car down, so the air leaked out from the hydraulic suspension line and the car gently rose to its proper 6cm ride height for scrutineering.
The really ingenious part is that Murray knew every other team would pick up on his device, so he put an empty aluminum box in the car with a few wires sticking out of it. Every other team focused on the box, and nobody noticed the hydraulic suspension line.
The whole system basically gave the car no suspension, making the Brabham brutal to drive, but fast enough to win the championship by a single point.
What's your favorite F1 cheat?