In a medium size saucepan, add potatoes, cover with water and cook until done, about 20 minutes.
Remove potatoes into a bowl and mash well; set aside.
Peel hard boiled eggs, mash well and add to mashed potatoes; mix well to incorporate.
In a large glass bowl, add cold water, mashed potato/egg mixture, grated cucumbers, grated radishes, chopped green onion, fresh dill weed, lemon juice, white vinegar, black pepper and salt; mix very well to blend.
Adust seasonings to taste.
Just before serving, add 6 ice cubes and let chill for about 10 minutes.