Let the players who play cricket be 12, the ones who play football 10, those who play only cricket are 6, then the number of players who play only football are ________, assuming there is $a$ total of 16 players.

Step 1 (Set Notation): Let $C$ be the set of players who play cricket, and $F$ be the set of players who play football. We are given:

• Total players $n(C\cup F)=16$

• Total cricket players $n(C)=12$

• Football players $n(F)=10$

• Players playing only cricket is $6$ (which is $n(C\setminus F)=6$)

Step 2 (Find intersection): The number of players who play only cricket is given by:

So 6 players play both sports.

Step 3 (Find only football): The number of players who play only football is:

Step 4 (Alternative Verification): Total players = (only cricket) + (both) + (only football):

Step 5 (Conclusion): The number of players playing only football is exactly 4.