There is a written rule: it's illegal. The Communications Act was amended in 1960 making it a federal offense for game shows to rig the outcome. Surreptitiously and intentionally removing the main prize on offer easily qualifies as just such a deceptive practice.
Unlawful behavior can be reasonably excluded from both the construction and the answers to logic puzzles, except when noted otherwise (or otherwise reasonable in context), which is why taking Monty hostage, busting through all three doors, jacking the car, snatching the goat, and driving off into the sunset, is not a reasonable response to the problem either, no matter how great TV it might make for.
https://www.visitthecapitol.gov/exhibitions/artifact/communi... if you need that in ink & vellum.
Unlawful behavior can be reasonably excluded from both the construction and the answers to logic puzzles, except when noted otherwise (or otherwise reasonable in context), which is why taking Monty hostage, busting through all three doors, jacking the car, snatching the goat, and driving off into the sunset, is not a reasonable response to the problem either, no matter how great TV it might make for.