Cluster method with binary variable

I need to do a cluster analysis for the following variables:

Trickquestion answer: Good/Wrong
count variable : range 0-9
time in minutes
count variable 
Number of observations: 3300

Since I am new to cluster algorithms I'm struggling with choosing the best cluster algorithm. I have read about the following methods:

• k prototypes
• k means with Gower's distance
• PAM algorithm.

For the cluster analysis I need to use R.

Can someone give advice about which methods suits the data best. Since I'm studying mathematics I need to give a full mathematical explanation, so a blackbox algorithm is not an option. Tips were I can find Mathematical information about the algorithms are also welcome.