This puzzle is from three weeks ago. Sorry for the delay. The gesture is dismissive, and there are a few possible one-word answers that could go along with it. Here are a few I thought of:
違う（ちがう）- with this word you are actively correcting what another person said. What they said is wrong, and you are swatting it out of the air.
大丈夫 （だいじょうぶ）- this one is used to dismiss something unnecessary. It may or may not be wrong, but either way you are “alright” without it.
いい – this word means “good,” of course, but I’ve written previously about its other meanings. Like 大丈夫, this dismisses something unnecessary.
In all the cases, the speaker would draw out the syllables for as long as he waves his hand. I wanted to make a video to show how this works but have had very little free time, so for now I’ll attempt to represent the intonation like so:
chigau → chiGAuuuu
daijoubu → DAIIIIjoubuu
ii → iiiiiiiiiiii
違う is most often used with the first facial expression – you’re angry that they are misunderstanding you. 大丈夫 and いい can probably be used with either, mostly the second, which was my attempt to represent surprise.
Only a few responses for this puzzle, but only Thomas kept his answers to single word responses. He offered 臭い, which I’ll accept, and だめ, which I think is strong but could also work. So, Thomas earns his second beer.