I'm planning the food for the celebration after the annual KCLMS tiddlywinks tournament (see WMC 408), but unfortunately I've forgotten some of the details.

I know that for every two people at the celebration we need one plate of chips, and that for every twelve people we need one plate of wafer-thin mints. I also know that we'll be serving plates of pizza and plates of jellied acorns, but I can't remember how many we need. I do remember, though, that each plate of pizza and each plate of jellied acorns will serve a whole number of people, and that we need more chips than pizza, more pizza than jellied acorns, and more jellied acorns than wafer-thin mints. Finally, I know that 360 people will be coming.

I asked my helpful assistant Phil if he could remember any more details, and he gave me the following annoyingly cryptic answer:

"The number of people at the party is the second-smallest possible so that we can serve exactly the right amount of all four kinds of food. Furthermore, we'll need to serve the smallest possible amount of food that is consistent with what you've remembered and the first piece of information I gave you."

Frankly, I don't have enough time to do maths when I have a party to plan! How many plates of each type of food do I need?