sorry Madame R. is a no-go. Hopefully this will help:
Griphook the Goblin can go, but Fleur Delacour cannot

Can Remus take Buckbeak to the moon?

Buckbeak is not allowed. Man, this one's harder than I thought it'd be. Hope these help you figure it out:
Prof. Grubbly Plank and Dennis Creevey cannot go, but Hedwig and Vernon can go

Can he take Narcissa or Bellatrix?

sorry, neither of those can go. any random guesses yet anyone?

I need a clue. Can Draco go?

remus can his students(ex) take student to the moon? (field trip!)
if not can he take lily and neville to the moon?

Can Remus take Dumbledore?

all of those can go

CAN- Harry, Ron, Hermione, McGonagall, Fred, Geoirge, Dudley, Griphook, Hedwig, Vernon, Albus, Lily, Neville, Draco, Petunia
CANT- Sirius, Himself, Grawp, Arabella Figg, Madame Rosmerta, Fleur, Buckbeak, Prof. Grubbly Plank, Dennis Creevey, Narcissa, Bellatrix

Can Remus take Lucius?

yes Lucius can come along

here's a hint: It has nothing to do with a certain arrangement of letters in the name or the fact that there is one letter in these names that there isnt in the others.

Huh? *feeling moreconfused than before.*

btt: Can Remus take Regulus to the moon?

Regulus cannot come

okay, this is the best hint that i could think of without giving it away: If you put them in order starting with the ones who can go, you might see a pattern. And what I was trying to say earlier was that the answer to who can come to the moon and who can't is the fact that is has nothing to do with certain letters in certain names.

Nope. Still completely in-the-dark. Can he take James?

yes James can come

CAN- Harry, Ron, Hermione, McGonagall, Fred, George, Dudley, Griphook, Hedwig, Vernon, Albus, Lily, Neville, Draco, Petunia, James
CANT- Sirius, Regulus, himself, Grawp, Arabella Figg, Madame Rosmerta, Fleur, Buckbeak, Prof. Grubbly Plank, Dennis Creevey, Narcissa, Bellatrix

okay, here's a set of more that can and can't come:
CAN-Ollivander, Percy, Susan, Quirrel, Flitwick, Hagrid, Norbert, Oliver Wood
CANT-Umbridge, Moody, Scrimgeour, Viktor, Collin Creevey, Barty Crouch Jr., Barty Crouch Sr., Igor Karkaroff

hope giving you those helped ya some

This is hard! Can he take Molly?

yes Molly can come

CAN- Harry, Ron, Hermione, McGonagall, Fred, George, Dudley, Griphook, Hedwig, Vernon, Albus, Lily, Neville, Draco, Petunia, James, Ollivander, Percy, Susan, Quirrel, Flitwick, Hagrid, Norbert, Oliver Wood, Molly

CAN'T- Sirius, Regulus, himself, Grawp, Arabella Figg, Madame Rosmerta, Fleur, Buckbeak, Prof. Grubbly Plank, Dennis Creevey, Narcissa, Bellatrix, Umbridge, Moody, Scrimgeour, Viktor, Collin Creevey, Barty Crouch Jr., Barty Crouch Sr., Igor Karkaroff

Can Remus take the rest of the Weasley's (Ginny, Percy, Bill, Arthur and Charlie)?

Ginny-yes
Percy-yes
Arthur-yes
Bill-no
Charlie-yes

Can Remus take only those who were in the PS/SS?

CORRECT!!!!!!!
next round's host is:

GRAHAM5980

Congratulations!

Thank you, thank you! *Takes a bow* I'll be here 'til I log off. *Winks* Try the nacho's, they're really good.

Okay, btt: Remus can take Harry, but not Ron to the moon.

can he take Hermione?