Peel potatoes and cut into small pieces. Heat water in a pot, and boil potatoes until tender, about 10-15 minutes. Strain and put potatoes in a large bowl. Add 1/2 tsp salt and vinegar, and mash slightly (leave some potato chunks). Let it cool.

Slice cucumbers to thin rounds, and cut carrots thinly (2" long). In a different bowl, sprinkle a little salt (not in the measurement) over cucumber and carrots, and let it sit for 2-3 minutes. Squeeze out water.

Cut boiled eggs into small pieces, and cut ham thinly (2" long strips).

Add vegetables, eggs, and ham to potatoes, then mayonnaise. Mix well. Add salt and pepper to taste.