Bob and Bob played golf against each other in a tournament. A marshall keeping their score had a difficult time because both players were named Bob. The scores the marshall recorded were the correct scores, but they may have been reversed. This is the way the marshall recorded their scores:
$$ \begin{array}{rcccccccccl} \mathrm{Hole:} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & \mathrm{Total} \\ \mathrm{Par:} & 4 & 4 & 5 & 3 & 5 & 4 & 3 & 4 & 4 & 36 \\ \mathrm{Bob A:} & 3 & 4 & 4 & 2 & 5 & 3 & 4 & 4 & 3 & 32 \\ \mathrm{Bob B:} & 4 & 4 & 7 & 4 & 3 & 4 & 3 & 5 & 6 & 40 \end{array} $$ When the match was over, the two Bob's glanced at the scorecard and complained.
Bob B said, "Wait a second, I had only one double bogey. And there was no way I lost by eight shots: I had fewer total shots until after we played the fifth hole."
Bob A said, "I had the eagle but I had only two birdies. I won only three holes.
an Eagle, Birdie, Bogey, and double bogey all refer to scores made on one hole. An eagle is two under par for the hole. A birdie is one under par. A bogey is one over par. A double bogey is two over par. A player wins a hole from the other player when he has the lower score for that hole.
Determine the correct hole-by-hole score for each player and their totals for the nine holes.
I have figured out that on hole 5 is swapped Bob A has 3 on hole 5 and Bob B has 5 on hole 5 because their is only eagle and Bob A has it. I'm confused on the rest...
You already figured out that hole 5 is switched. The other information you have about possible switches is the followin:
Further criteria that the switches have to meet are
Based on the above information, the holes we switch have to contain one number from the set $\{3,9\}$, two numbers from the set $\{1,3,4,6,9\}$, and three numbers from the set $\{1,3,4,6,8,9\}$. For instance, we can't switch both $3$ and $9$ because that would choose two numbers from $\{3,9\}$. Another example, is that we can't switch $1$, $3$, and $6$, since that would choose three numbers from $\{1,3,4,6,9\}$ and we can only have two from that set.
Suppose we choose $1$, $3$, and $8$. That gives a total for the first five holes of $22$ and $18$ for BobA and BobB, respectively. However, that also gives BobA three birdies when he can only have two.
Suppose we choose $3$, $4$, and $8$. Then again it satisfies the five hole total requirement but also gives BobA three birdies, which is not allowed.
Suppose we choose $3$, $6$, and $8$. Then we again satisfy the five hole total requirement. It also gives BobA two birdies and has him winning three holes. It also has BobB losing by $2$ shots and not $8$. It therefore meets all the given requirements and will give the correct score card.