2, 4, 6: NO
2, 2, 2: NO
0, 1, 2: NO
900, 600, 300: NO
-1, 0, 1: NO
a, b, c: INVALID
Well, that's some obvious theories that don't seem to be on the right track at all. Back to basics, then: does the rule output the same judgment every time you give it the same input?
2, 4, 6: YES
- and there's an obvious theory (any set is allowed the second time, but not the first) which does seem to be on the right track, but she's met Keltham so she's SUSPICIOUS it's more complicated than that. For example, maybe it'll be allowed the second time but not the third, or maybe the second time it gets evaluated by a different rule than it did the first time, but the different rule might not always return 'yes'?
-1, 0, 1: YES
6, 4, 2: NO
2, 4, 6 for the third time?: YES
6, 4, 2: YES
2, 4, 6 for the fourth time?: YES
2, 2, 2: YES
-2, 45, 1: NO
-2, 45, 1: YES
1e16, 1000, 4: NO
1e16, 1000, 4: YES
...on the other hand sometimes the rule is in fact simple and you shouldn't overthink it.
She submits her guess.
She's done first. What kind of bizarre nonsense is everyone else getting up to?