In this world, there are 10 types of people --
    those who understand the significance of the date 11/11/11 to
        Gene Upshaw, Kevin Gregg, Jeff Saturday, Willie Lanier,
        and Mike Ribeiro;
    and those who don't.

Explain.

Solution to the Problem:

Since there are only two possibilities for the types of people,
10 must be in base two (where 10 represents 2).
In base 2, the number 11 11 11 represents the base ten number 63,
which was the jersey number of the five players listed above.

Correctly solved by:

1. James Alarie Flint, Michigan
2. Chad Fore Gate City, Virginia
3. Blace Martin Mountain View High School,
Mountain View, Wyoming
4. Trey Briggs Mountain View High School,
Mountain View, Wyoming
5. Bo Aimone Mountain View High School,
Mountain View, Wyoming
6. Austin Hale Mountain View High School,
Mountain View, Wyoming
7. Alyssa Sibelrud Mountain View High School,
Mountain View, Wyoming