The 15 winners of a contest have been invited to a congratulatory party.
Although the average age of the group (i.e., the mean) is exactly 25,
    some of the winners are quite young (15, 16, and 17).
The host asks the whole group to wear nametags with their names and ages.

Shortly after the party begins, three gatecrashers sneak in, fill out blank
    nametags with their own names and ages, and mingle with the legitimate guests.
Below are the 18 nametags.
Can you identify the 3 gatecrashers?

Al, 33    
Bev, 15  
Carl, 22
David, 26
Ed, 23    
Fran, 20
Guy, 19  
Heidi, 25
Irv, 32  
John, 24
Kate, 18
Les, 21    
Mark, 35
Nancy, 31
Oscar, 16
Patty, 17
Quincy, 28
Richard, 27

Solution to the Problem:

The Gatecrashers are Kate (18), Guy (19), and Fran (20).

The sum of the ages on all 18 nametags is 432.
The average age of the 15 legitimate guests is 25,
    so the sum of their ages must be 15 x 25 = 375.

Therefore, the sum of the three gatecrashers must be 432 - 375 = 57.
The average age of the gatecrashers must be 57 / 3 = 19.
Since we were told that the 15-, 16-, and 17-year olds are legitimate guests,
the youngest gatecrasher must be 18, and the other two must be 19 and 20.

Correctly solved by:

1. Makayla Wisenbaker Mountain View High School,
Mountain View, Wyoming