Given information:
- Total number of students in the class = 33
- Number of students playing cricket = 20
- Number of students playing football = 25
- Number of students playing volleyball = 18
- Number of students playing both cricket and football = 15
- Number of students playing both football and volleyball = 12
- Number of students playing both cricket and volleyball = 10

To find the number of students who play only one game, we can use the principle of inclusion-exclusion.

Step 1: Find the total number of students playing at least one game.
- Number of students playing cricket = 20
- Number of students playing football = 25
- Number of students playing volleyball = 18

Using the principle of inclusion-exclusion:
Total = (Number of students playing cricket) + (Number of students playing football) + (Number of students playing volleyball) - (Number of students playing both cricket and football) - (Number of students playing both football and volleyball) - (Number of students playing both cricket and volleyball) + (Number of students playing all three games)

Total = 20 + 25 + 18 - 15 - 12 - 10 + (Number of students playing all three games)

Step 2: Find the number of students playing all three games.
We can find this by subtracting the total number of students playing only one game or two games from the total number of students playing at least one game.

Number of students playing all three games = Total - (Number of students playing only one game or two games)

Step 3: Find the number of students playing only one game.
Number of students playing only one game = (Number of students playing cricket) + (Number of students playing football) + (Number of students playing volleyball) - 2 * (Number of students playing all three games)

Now, let's substitute the given values into the equations and solve for the number of students playing all three games and the number of students playing only one game.

Total = 20 + 25 + 18 - 15 - 12 - 10 + (Number of students playing all three games)
Total = 26 + (Number of students playing all three games)

Number of students playing all three games = Total - 26

Number of students playing only one game = 20 + 25 + 18 - 2 * (Number of students playing all three games)

Substituting the value of "Total" from the first equation into the second equation:
Number of students playing only one game = 20 + 25 + 18 - 2 * (Total - 26)
Number of students playing only one game = 63 - 2 * Total + 52
Number of students playing only one game = 115 - 2 * Total

Now, let's substitute the value of "Total" from the first equation into the third equation:
Number of students playing only one game = 115 - 2 * (26 + Number of students playing all three games)
Number of students playing only one game = 115 - 52 - 2 * Number of students playing all three games
Number of students playing only one game = 63 - 2 * Number of students playing all three games

Since the number of students playing all three games cannot be negative, the maximum value it can take is 10 (when all the students play all three