DeletedUser
Guest
Grass+grass+Cerberus= Chain Lightning NOT Biremes
The first problem is that there is not 6 combinations per group of 3. (Those are "Permutations", and are only used if order is important. In the cauldron, just like in your ice cream sundae or your pizza toppings, it does not matter which is first or second or third. HOOF GRASS TOOTH gets the same reward as GRASS TOOTH HOOF.)
The second problem is that here, there is "replacement". Your Combination formula is used with "no replacement". (The idea of replacement comes from the old story problem where you're pulling marbles out of a bag. If you put it back in, you can select the same color more than once.) Here, we can have the same ingredient more than once (GRASS GRASS GRASS), so we call it "with replacement" since you "put the grass back in the bag" so that it was possible to pull it out again.
The proper formula is:
(n + r - 1)!
-----------
r! (n - 1)!
n = 8, r = 3....
8 + 3 - 1 = 10!
----------- ---
3! (8 - 1)! = 3! 7!
10 x 9 x 8
-----------
3 x 2 x 1
720
---- = 120 different Cauldron Combinations.
6
I have 107 mapped out already... the last 13 are:
TOOTH TOOTH QUICKSILVER
GRASS GRASS QUICKSILVER
GRASS GRASS CLAWS
FEATHERS FEATHERS TOOTH
FEATHERS QUICKSILVER QUICKSILVER = Horseman Reinforcement VIII
FEATHERS TOOTH GRASS
AMBROSIA SCALES CLAWS
AMBROSIA HOOF HOOF
AMBROSIA HOOF SCALES
AMBROSIA GRASS QUICKSILVER
AMBROSIA TOOTH QUICKSILVER
AMBROSIA FEATHERS CLAWS
AMBROSIA FEATHERS SCALES