Number Choosing Contest.

3^2

5*2

10+1

1100 (base 2)

baker's dozen

9: breaks XYZ & 2, 3, 4 and 5.
10: breaks XYZ & 4 and 5.
11: breaks XYZ & 2, 4 and 5.
12: breaks XYZ & 2, 4 and 5.
13: breaks XY & 4 and 5.