**The structure of Noun Phrases** Simple noun phrases usually have two sections, a Determinative and a Head. The Determinative function is typically carried out by special words called *DETERMINERS*. The Head function is usually carried out by a phrase headed by a noun. This type of phrase we see inside a noun phrase is called a *NOMINAL*. In the phrase *a big dog*, we see the following structure: ![enter image description here][1] Now, because the nominal is a proper phrase in its own right, it has its own internal structure. Like all phrases, it has its own Head. It also very often has a Modifier. When this Modifier comes before the head, we call it an *Attributive* Modifier. Attributive Modifiers are very often adjectives. In the phrase *big dog*, the Modifier is the adjective, *big*, and the Head is the noun, *dog*. Now, notice that I said that Determinatives are "typically" determiners, and that Modifiers are "often" adjectives. This is because other types of words and phrases can carry out these jobs. For example in the noun phrase: - John's Madonna t-shirt ... the Determinative is the genitive noun phrase *John's*, not a determiner. Similarly, the Modifier in the nominal is the proper noun, *Madonna*, not an adjective. Notice also that both determiners and adjectives can carry out other functions apart from Determinative, or Attributive Modifier: - That was **the** fastest I ran. - **Indignant**, she waltzed out of the room. ***Each* versus *Every*** One of the other answers here brings up a comparison with *each* and *every*. At first blush, this seems quite reasonable. Firstly, both *each* and *every* are determiners. They also have some similarities in terms of meaning. For example, we can say that they sometimes give us a meaning somewhat similar to *all*: - All the men have finished their food. - Every man has finished their food. - Each man has finished their food. The sentences above basically give us the same kind of information. There are no men who haven't finished their food. Notice from the sentence above that *each* and *every* have some similar grammatical properties too. For instance, they both take singular nouns: in the examples above we see "all the *men*", but "every *man*" and "each *man*". This is because *every* and *each* have *DISTRIBUTIVE* meanings. We consider that the verb phrase *finished their food* applies to each member of that group of men considered individually. Another difference you might have noticed is that in the first example, *all* occurrs with the determiner *the*. The word *all* differs from prototypical determiners because it can occur with a different function in a special slot before the Determinative. Writers like Quirk et al (1985), call words like *all* "pre-determiners". Determiners like *each* and *every*, *the*, *a*, *this*, *no* and also genitive noun phrases such as *his*, *ones* and *Ben's* have an important property: we can only have one of these types of words in Determinative function. The following phrases where we find two such words in Determinative function are therefore badly formed: - *The my dog is wagging its tail. - *A my friend is coming. - *The every man finished their meal. - *Each the book was shelved properly. - *No Ben's friend came to the party. So we've seen that *each* and *every* have some similar properties: they're both determiners; semantically they have distributive meanings similar to *all*; they cannot occur in determinative function together with other central determiners or with genitive noun phrases. However, at this point all similarity ends. *Each* and *every* have other semantic and syntactic properties which make them very different. We shall see that just because we can use *every* in a particular way, it does not mean we can therefore use *each* in that same way - or vice verse. First of all, we can use *each* to stand in for an *each* + [noun] combination. We can't do this with *every*: - Give me one of each. - *Give me one of every. (ungrammatical) Because of this we can use *each* on its own as an Adjunct after the Subject in sentences such as: - The baboons each gave the elephant a donut. - *The baboons every gave the elephant a donut. We can also therefore use *each* and not *every* on their own in partitive expressions: - Each of them ... - *Every of them ... A second difference that's important in terms of syntax is that we can freely modify the word *every*, but not the word *each*: - *Almost each dog ate a bone. - Almost every dog ate a bone. In the first example we see *each* modified by the word *almost* with bad results. The example with *every* is fine. There are many, many more differences between *each* and *every*, but, for the moment, I'll mention just one more: we can use *every* without a distributive meaning, mostly with abstract nouns. When we use it like this, it has a "multal" meaning. In other words it means something like "a lot of": - We gave him encouragement. - We gave him every encouragement. - *We gave him each encouragement. We can see the non-count use of *encouragement* in the first example above. In the second example we see the same non-count use of the word *encouragement*. This example does not mean that there was a group of encouragements and we gave him all of them. It means we gave him a lot of encouragement or a variety of encouragement. The last example cannot mean the same thing. *Encouragement* here cannot be that non-count sense of encouragement. The determiner *each* cannot have a multal instead of distributive meaning. **The Original Poster's question** > *The set of elements **whose each** pair is ... (ungrammatical) The sentence above is ungrammatical. The reason is, simply, that *whose* is a genitive noun phrase, just like *his* or *Ben's*. We have already shown further above that *each* and *every* cannot be used together with genitive pronouns in Determinative function. I fact *whose*, like other genitive noun phrases, cannot be used with central determiners as Determinatives at all: - *A man whose the dogs bit him went to the hospital yesterday. - *The dictionary whose a page you tore out is missing. - *The elephants whose their donuts you ate has escaped. - *That man whose every toe was amputated went to the police. - *The wife whose each husband died in mysterious circumstances absconded. The sentences above are all badly formed. They each try to use *whose* with another genitive noun phrase or determiner as a Determinative. Some of the other comments here have noted that we can use *whose* with *every* in phrases like: - whose every move (grammatical) We can also use *every* after other genitives such as *his* or *her*: These posters argue that if *whose every move* is grammatical, then *whose each move* must also be grammatical. This does not follow though, because as we have shown, *each* and *every* do not have the same grammar. However, in any case this really isn't the key issue here anyway. The Original Poster's example is clearly asking about using *whose each* as a Determinative. We have shown that this is not possible. The phrase *whose every move* does *NOT* use *every* as a Determinative, it uses it as a Modifier in the nominal *every move*. The word *each* cannot appear alone in this function. The structure for the phrase *whose every move* is: ![enter image description here][2] As the *Cambridge Grammar of the English Language* (Huddleston & Pullum, 2002) states in its section on *every* versus *each*: >> (g). *Every*, but not *each*, can occur as a modifier following a genitive [...]. >>[25] a. *They scrutinised [her every move]*. b. * *They scrutinised [her each move].* The [ * ] next to example (b) there indicates that it is ungrammatical. Example (a) is structured [her] [every move]. It is similar in meaning to "[every move] of hers". This clearly shows that we cannot use *each* as a modifier after genitives such as *her* or *whose*. (We can however use the idiomatic phrase *each and every*, which patterns the same as *every* here). **NOTES**: 1. I'm assuming that readers know that we can use relative *whose* to refer to both people and object. I won't address this here, Fumblefingers has links to relevant posts on that subject in his answer, if you'd like to read about it. 2. I use the term *Determiner* in this piece, like the majority of modern grammars, to refer to the class of words. I use *Determinative* to refer to the function. Huddleston and Pullum reverse the established terminology in CGEL. 3. John Hanna and Fumblefingers state in comments or posts that for them *whose each* is grammatical. It might be the case that *whose each* is grammatical in the OP's intended usage for speakers of some varieties of English. I'm most familiar with so-called Standard GB, and it might be that *whose each* is grammatical for some other groups of speakers. [1]: https://i.sstatic.net/mxtVH.png [2]: https://i.sstatic.net/SX0qV.png