[zenobia43]

After entering all the Xs from the initial clues and the positive from clue 7, you can prove that Monday = Kailey = black and white = Cassiopeia.

Using clues 2, 3, 5, and 6, prove that Monday = Cassiopeia.

Clue 2: Endymion cannot be Monday because clue 2 implies that they are different people.
Clue 3: Agamemnon cannot be Monday.
Clue 5: Hephaestus must either be Wednesday or chocolate chip and chocolate chip cannot be Monday (clue 2). So Hephaestus cannot be Monday.
Clue 6: Eurydice cannot be Monday because clue 6 implies that they are different people.

So Cassiopeia = Monday.

After filling in the implications of Cassiopeia = Monday in the DC category block (the intersection of cookies and mythological names), you will see that Agamemnon = peanut butter.

Clue 2: Endymion cannot be peanut butter because the clue implies that they are different people.
Clue 6: Eurydice cannot be peanut butter because the clue implies that they are different people.
Clue 9: Hephaestus cannot be peanut butter.
Clue 2: Cassiopeia is Monday and clue 2 implies that Monday and peanut butter are different people. So Cassiopeia cannot be peanut butter.

So Agamemnon = peanut butter.

After filling in all the implications, we now see that Braydon can only be Hephaestus.

Clue 2, 6: Braydon cannot be Endymion or Eurydice.
Clue 2, 6: Braydon cannot be Cassiopeia because Cassiopeia is Monday and Braydon cannot be Monday.
Clue 2, 6: Braydon can no longer be Agamemnon because now Agamemnon is peanut butter, and Braydon cannot be peanut butter.

So Braydon = Hephaestus.

Using clue 6 some more and the implications from the existing positives, we see that Endymion = gingerbread, and the DC category block is easily completed.

Then using clue 4 and all the accumulated implications we can prove that Kailey = Monday.

That completes our proof that Monday = Kailey = black and white = Cassiopeia.

Once we know Kailey = Monday, we know immediately from clue 4 that Janiyah = Tuesday.

Notice how we used clues 2 and 6 many times to get to this point. This is the gist of suprstarB08's post. There was a lot of information in those two clues.

If you get stuck, and assuming that you haven't misplaced an X somewhere, recheck clues that have the form seen in clue 5. There is usually more information there than you can see at first glance.