Chuck Cheddar's balloon is nowhere to be seen after he arrives at the conference.
Any plumber trying to diagnose and fix a sink that won't drain would inspect the drain pipes first before using a plunger; thus Rock, Paper, and Scissors should have noticed the clog as soon as they had a look at the pipes, and they should have been able to fix it. Sam should not have had to fix it - the plumbers would have done it already.