Given Information:

- Total number of students surveyed = 300
- Number of students who like to play cricket = 125
- Number of students who like to play football = 145
- Number of students who like to play tennis = 90
- Number of students who like to play exactly two games out of the three games = 32

To find:

- Number of students who like to play all the three games

Solution:

Let's represent the number of students who like to play all three games by "x".

From the given information, we can create the following Venn diagram:

```
Cricket (125)
/ | \
/ | \
/ | \
Football (145)--------Both--------Tennis (90)
\ | /
\ | /
\ | /
Neither (48)
```

We can see that:

- Number of students who like to play at least one game = 125 + 145 + 90 = 360 (Note that some students may like to play more than one game)
- Total number of students surveyed = 300

This means that some students like to play more than one game. Let's find out how many such students are there.

- Number of students who like to play exactly two games out of the three games = 32

We can see from the Venn diagram that the number of students who like to play exactly two games is the sum of the three regions where two circles overlap:

- Number of students who like to play cricket and football only = ?
- Number of students who like to play cricket and tennis only = ?
- Number of students who like to play football and tennis only = ?

Let's find these values one by one.

- Number of students who like to play cricket and football only:

From the Venn diagram, we can see that the region where only cricket and football overlap is "Both - x". So:

Both - x = ?
Both = 32
x = Both - 32 = ?

- Number of students who like to play cricket and tennis only:

From the Venn diagram, we can see that the region where only cricket and tennis overlap is "Both - x". So:

Both - x = ?
Both = 32
x = Both - 32 = ?

- Number of students who like to play football and tennis only:

From the Venn diagram, we can see that the region where only football and tennis overlap is "Both - x". So:

Both - x = ?
Both = 32
x = Both - 32 = ?

Now, we can find the number of students who like to play all three games:

- Number of students who like to play at least one game = 360
- Number of students who like to play more than one game = (cricket and football only) + (cricket and tennis only) + (football and tennis only) + x
- Substituting the values we found above, we get:

Number of students who like to play more than one game = ? + ? + ? + x
Number of students who like to play more than one game = (Both - x) + (Both - x) + (Both - x) + x
Number