In the spelling bee competition, every player plays against every other player four times. Every player plays the same number of games. There are a total of 220 games played. How many players are there?
Assuming if each player does only one game,
When the total number of players is 1, there is 0 game.
When the total number of players is 2, there is 1 game.
When the total number of players is 3, there are 1 + 2 games.
When the total number of players is 4, there are 1 + 2 + 3 games.

Note that the total number of players is 1 more that the last digit in the string of addition.

Let the last digit in the string of addition be 1 u.

Every player plays against every other player four times. 
Total number of games = String of addition x 4.

(1 + 2 + 3 + ... + 1 u) x 4 = 220
(1 + 2 + 3 + ... + 1 u) = 220 ÷ 4
(1 + 2 + 3 + ... + 1 u) = 55

Formula:
Sum of numbers
= 1 + 2 + 3 + ...+ last digit
= ^{last digit x (last digit + 1)}₂

^{last digit x (last digit + 1)}₂ = 1 + 2 + 3 + ...+ last digit
^{1 u x (1 u + 1)}₂ = 55
1 u x (1 u + 1) = 55 x 2
10 x 11 = 110

1 u = 10

Last digit in the string of addition is 10.

Number of players = 10 + 1 = 11

Answer(s): 11