You stand before a panel with two buttons on it. One of them will dispense your favorite beverage, and you're dying for a sip. The other will destroy all life throughout the universe, so you'd really rather not press that one. You don't know which button is which, but fortunately the buttons have three alien attendants--each a different race--to help you. You know a little bit about the alien languages, but unfortunately you don't know which alien uses which language. The aliens are identified with signs reading "1", "3", and "6".
The aliens' languages are based on gestures, and there are four polite ways to ask a question: point with the left index finger, the left index finger and middle finger, the right index finger, or the right index finger and middle finger, for 50 seconds. Any other form of gesture would be considered rude, and would cause the aliens to immediately shoot you (which would be bad).
One of the aliens is an Altairian. If you ask a question by pointing with your left hand (one or two fingers), it will (after 49 seconds) nod its head if the left button dispenses a beverage and do nothing if it does not. Likewise if you ask a question by pointing with your right hand, it will not its head if the right button dispenses a beverage and do nothing if it does not.
One of the other aliens is a Denebrian. If you ask a question by pointing with one finger (either hand), it will (after 49 seconds) nod its head if the alien with the closer number is an Altairian or else do nothing. If you point with two fingers (either hand), it will nod its head if the further number is an Altairian or else do nothing.
The remaining alien is a Snoozorian. It's going to sleep for the next five years no matter what you do, and can thus be counted upon to simply do nothing.
You've been called to battle, and need to leave within the next two minutes, but you really want your beverage before then. This wouldn't be enough time, had you not learned in your latest linguistics class that it's possible to politely address two aliens simultaneously subject to the following constraints:
One must simultaneously use both arms to address the aliens, with one arm pointed at each; the arms must not be crossed, and one must continue to point with both arms for the full 50 seconds.
If you ask questions which both merit affirmative responses, the aliens will get annoyed and shoot you (again, not good).
Note: This is my first attempt at formulating a variation of a "Lady or the tiger" puzzle; rather than make some of the guardians deceitful, I decided to instead make them vary in the questions they answer. Since only one alien knows where the right button is, and since the first alien one talks to might not know anything, it's necessary to be able to talk to all three aliens, but being able to simply ask a question of each without restriction doesn't seem very satisfying. If people like the concept, but not the particulars, I'd be open to advice on how to make the puzzle more interesting and/or satisfying.