After kicking one coach likes to play practice games with 6 players on each team she doesn’t like any team to have more or fewer than 6 players and she doesn’t like anyone to be left off a team what are the possible numbers of players who must show up to practice so that the coach can make these teams
In order for the coach to make teams with 6 players on each team, the total number of players must be a multiple of 6. Additionally, she does not want anyone to be left off a team, so the total number of players should not exceed the maximum number of players that can be divided into teams of 6.
The possible numbers of players who must show up to practice, given these conditions, are as follows:
- 6 players: There can only be one team with 6 players.
- 12 players: Two teams of 6 players each.
- 18 players: Three teams of 6 players each.
- 24 players: Four teams of 6 players each.
- 30 players: Five teams of 6 players each.
- 36 players: Six teams of 6 players each.
Any number beyond this will result in uneven teams or someone being left off a team.