Number Choosing Contest.

I think I've got rule 2 down.

It is the easiest of the lot, I think, followed by 4 and then probably 3. I'm not sure which of 1 and 5 is more cruel. They're both pretty mean.

Time to fill more integers, anyway

27, 29, 31, 33, 35

27: breaks YZ & 1, 2, 4 and 5.
29: breaks YZ & 2 and 4.
31: breaks YZ & 1 and 4.
33: breaks YZ & 1, 2, 4 and 5.
35: breaks YZ & 2, 4 and 5.

Okay so there has to be a large number that meets rule 1.

Because if I understand rule 2 and 4 there are no numbers less than 100 that meet both.


99

98

97

46189

130321

99: breaks YZ & 1, 2, 3, 4 and 5.
98: breaks YZ & 1, 2, 3 and 4.
97: breaks YZ & 1, 3 and 4.
46189: breaks YZ & 1, 2 and 3.
130321: breaks YZ & 1, 2 and 3.

Does that back up your hypotheses? *wink*