Number Choosing Contest.

Still no clue about even rule 2.

26

27

28

29

30

26:
Breaks rules 2, 3, and 4

27:
Breaks rules 1, 3, 4, and 5

28:
Breaks rules 3 and 4

29:
Breaks rules 4 and 5

30:
Breaks rules 2, 3, 4, and 5

That last batch would appear to contain counterexamples to my ideas for rules 2 and 3. Hmph.

31

32

225

811

50625

31:
Breaks rules 2 and 5

32:
Breaks rules 2, 3, 4, and 5

225:
Breaks rules 3, 4, and 5

811:
Breaks rules 4 and 5

50625:
Breaks rules 3, 4, and 5