Hey testtrail429.

As a hint to start off, consider ten combinations that correspond to have 0,1,2,3,4,5,6,7,8, and 9 in the lowest digit (for example $1.98 would have an 8 in this category) so basically this is given when you have N cents in total and to get this attribute you calculate N % 10 where % is the modulus function.

Now consider that to get back the change you need to have a combination of these coins to be the change: so if the change is C then C - 3*x - 5*y = 0 for positive numbers (including zero) to get back your change, otherwise if this is not possible then you can't get the change back.