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So when you want to buy all of the donuts in a shop, but only one of each. You say: I want all of the donuts. The employee then ask you "all of them?" You tell him "No, one of each." Is there a faster way, a more concise way to say this in one spurt?

I respectfully disagree with the other answers. Your question is asking for a concise wording, and there is an equally clear and more concise way to express what you want (but please, read my notes at the bottom, and read all the other answers and comments as well).

My answer

In the context of speaking to a person who sells different kinds of doughnuts, this wording is completely clear:

One of each doughnut(, please).

It's not necessary to explicitly say "each kind of doughnut" at all, if you want to be concise. "One of each doughnut" can only be understood one way, and if someone spends their day selling doughnuts, I'll bet dollars to them that they hear this kind of phrasing often.

One each of chocolate, cream-filled, and rainbow sprinkles, please.

Three each of cinnamon and vanilla icing, thanks.

Two of each iced doughnut, thanks.

The exact thing you're referring to isn't important here—doughnuts, pizzas, flowers, anything that is in obvious groups, types or kinds would make sense this way.

One each of Hawaiian and Pepperoni to take away, please.

I can't decide between your cakes! One slice of each, please!

Even shorter

As pointed out in other answers and comments (too many names to mention directly), there may be an even more concise option:

One of each (, please)

This would probably be understood just fine in context, so long as you're standing in a shop that really does sell nothing but doughnuts. I really cannot imagine that shop—but yes, if it is a really specialized business, that would be fine. And worst case, here's your conversation:

One of each, please.

You want one of every doughnut and muffin?

Oh, no, sorry. Just the doughnuts, thanks.

No problem.

This exchange is not more concise than your example in the question, but it is a successful communication event without meaningful misunderstanding, and is the kind of conversation a shopkeeper has all the time.

Why is there so much debate on this question?

Comments aren't the right place for extended discussion. So for the benefit of future learners reading this, I want to briefly discuss some reasons why I'm so comfortable with one of each doughnut, and why so many other people here aren't.

This is not meant in the spirit of debate and riposte; it's meant as a brief didactic look at some points and counterpoints. Nor is it intended to be exhaustive, definitive, or to rebuke any of the disagreements.

Concise vs precise

Communicating concisely is different to communicating precisely. Even if the question hadn't explicitly asked for a concise wording, in casual speech speakers err towards more concise, less precise wording almost without exception.

Real-world spoken English is more holes than it is cloth. English speakers enthusiastically drop out pretty much anything that can be understood from context, create new contractions, and commit all kinds of grammatical sins, and yet they are still consistently understood. They don't do it consciously, and when they hear another person speaking that way in the real world, they don't think about it consciously either. We rarely need to be precise in speech, and so we usually choose to be concise.

Context is king

All communication is about context. If the question was: "I want to order doughnuts over the phone from a bakery that sells all kinds of pastries and desserts," then the answer would be very different. Some of the answers here have made different assumptions about the context of the dialogue. If it isn't obvious what you're asking the person for, you'll need to be more precise about how you ask.

Polite and impolite speech

Generaly speaking, in English, polite speech uses more words. Many languages have a grammatical way to speak formally or politely to someone—for example, second person plural (like French), third person (like Italian), even totally different vocabulary and grammar (like Japanese).

English doesn't have a single, clear grammatical rule about politeness that's the same everywhere. What is polite and what is rude changes in deferent contexts, and it changes a lot in different places. If you accidentally speak impolitely, it will prevent you from being understood clearly (and will also just not be nice).

So if it isn't common where you are to drop the words kind of from a phrase like one of each kind of doughnut, then you're going to sound both confusing and rude. As a learner, it is good advice to be careful about being too concise.

Just 3-5 Words Needed

If it's a donut shop in the US, the phrase one of each is usually sufficient. The rest is just tacking on politeness or disambiguation. Even if the store also sells crullers and other things, Donuts, please. One of each. would be reasonably polite and unambiguous. For example:

Cashier: Welcome to Week-Old Donuts. What would you like?

Customer: Donuts, please. One of each.

Cashier: Coming right up.

Another variant:

(I want / I'll buy) one doughnut of each kind (that you have / that's for sale) (, please).

Everything in the parentheses is optional, but useful, though.

For even shorter than that, you will need to search a different language :)

You can say "I want one of each of your doughnuts".