The possibilities for the number of days Caleb could play the game without repeating a level are 1, 2, 3, 4, 6, and 12 days.
If Caleb plays the same number of levels each day and completes the game without repeating a level, we can find the possible combinations by considering the divisors of the total number of levels, which is 12.
The divisors of 12 are: 1, 2, 3, 4, 6, and 12.
Let's see the possibilities for the number of days Caleb could play the game without repeating a level:
If Caleb plays 1 level per day, he will finish in 12 days.
If Caleb plays 2 levels per day, he will finish in 6 days.
If Caleb plays 3 levels per day, he will finish in 4 days.
If Caleb plays 4 levels per day, he will finish in 3 days.
If Caleb plays 6 levels per day, he will finish in 2 days.
If Caleb plays 12 levels per day, he will finish in 1 day.
So, these are the possibilities for the number of days Caleb could play the game without repeating a level: 1, 2, 3, 4, 6, and 12 days.