Allison: I remember how much fiber it has.
Brook: I remember how much sugar it has.
Cameron: I remember how much protein it has.
Digby: I remember how much fat it has.
Eli: I remember how much saturated fat it has.
Frankie: I remember how much carbohydrate it has.
Cameron: well we each know a little more: after all, saturated fat is a type of fat, and both fiber and sugar are types of carbohydrate.
Digby: Yeah - and each gram of fat has 9 calories, while each gram of carbohydrate or protein has 4 calories.
Eli: Okay, so who knows what? Remember to take everything anyone has already said into account.
Allison: Nobody else knows fiber. (FIBER>1)
Brook: Nobody else knows sugar. (SUGAR>1)
Cameron: Someone else could know protein. (10>PROTEIN>0)
Digby: Now we all know that Frankie knew protein and fat.
Eli: Someone could know the saturated fat. (SAT=1)
Frankie: Well now everyone knows the saturated fat; but still, only Digby and I know the fat. (FAT>3)
Allison: Nobody else knows fiber, but now that I've said that, someone could know it. And now that I've said that, of course, everyone knows it. (FIBER=3)
Brook: So now Frankie and I know everything. Here's a hint: there exists a pair of equal values. (Reduces to 10 sets of possibilities)
Cameron: I still don't know fat. (Reduces to PROTEIN=1,3,7)
Digby: I still have three possible sets of values. (FAT=7,15)
Eli: Well I can't contribute at all; Frankie, bring us home.
Frankie: None of the values have a 7 as a digit. (FAT, PROTEIN aren't 7, SUGAR isn't 17)
Allison: Well let's get these for Mr. Lucas, ASAP! (Because it's 3,15,3,15,1,19, or COCOAS)