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On day 1, i'm going to run 12 laps at the fitrec. then, for each of the next six days, i'm going to roll a six-sided die, and then run that many more laps than i ran the previous day. for example, i may end up running this sequence of laps: (12, 16, 21, 22, 23, 25, 30). how many different possible 7-day sequences of this form are there?

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MuchoE
Short answer: 36.
This is a combination/permutation problem.
To put it simple, a die has 6 sides, there are 7 days but 1 is already determined (12 laps).
So if we multiple the options (sides on a die) × the number of days (6) we get:
6 × 6 = 36 possible outcomes.

To show this we can get
12, 13, 14, 15, 16, 17, 18
12, 13, 14, 15, 16, 17, 19
12, 13, 14, 15, 16, 17, 20
... all the way to
12, 18, 24, 30, 36, 42, 48

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