For 26.b try paying for the amounts mentioned in part a without giving any change. That should give you an idea of how to find the greatest amount you cannot pay for.

On 27, remember all divisors of $n$ can be paired with another divisor so that their product is equal to $n$. Knowing this, how many divisors should the number have? Once you find the number of factors the number should have, it will be useful to remember how to count the number of factors of a given number to try to find the possible numbers.

For 28, try finding out a pattern of the numbers $1!$, $1! + 2!$, $1! + 2! + 3!$, etc. This should help you find conditions for $x$ and $y$.

On 29, split the set of numbers in two categories: multiples of $3$ and not multiples of $3$. How many of each do you have? When you select the $k$ numbers from the original set, what is the "worst" that could happen?

Let us know if this hints helped or if you need additional hints.