To make the dressing, whisk together the vinegar, olive oil, and sugar in a small bowl. Add salt and pepper, to taste.
Toss the dressing on to the cucumber. Cover, and store the salad in the fridge until you are ready to serve the chickpea patties.
Note: you want the cucumbers to sit in the dressing for a good half an hour to hour before serving.
When you are ready to serve the salad, toss in the fresh mint.