MathDB

Mr. Murgatroyd decides to throw his class a pizza party, but he's going to make them hunt for it first. He chooses eleven locations in the school, which we'll call

1, 2, \ldots, 11

. His plan is to tell students to start at location

1

, and at each location

n

from

1

10

, they will find a message directing them to go to location

n+1

; at location

11

, there's pizza!
Mr. Murgatroyd sends his teaching assistant to post the ten messages in locations

1

10

. Unfortunately, the assistant jumbles up the message cards at random before posting them. If the students begin at location

1

as planned and follow the directions at each location, show that they will still get to the pizza.

Problem Statement