February 18, 2014
Lainie has misplaced her shoes again. They are somewhere in Saint Ann's inside a room numbered one through eleven and on a floor numbered one through eleven. Several of her friends in the math department remember seeing them. Anna recalls that both the room and floor numbers are prime. Michael remembers that the room and floor numbers have a sum that is both a multiple of three and a multiple of four. Richard remembers that the room and floor numbers are of opposite parity, that is, one of them is even and the other is odd. Kevin remembers that the difference between the room and floor numbers is three. Simon recalls that the floor number is greater than the room number. Anna's 6th grade math class knows where Lainie left her shoes and they declare that exactly one of the math teacher's recollections is inaccurate. Where are Lainie's shoes?