Place 4 cups of water in a 4 quart (thick bottomed) pan on medium/ high heat. Bring to boil and drop chunks of potatoes in water (make sure water covers potato chunks). Lower heat to medium/ low, cook until tender, about 10 minutes.
MEANWHILE: Combine mayonnaise, mustard,vinegar and sugar in medium bowl. Set aside.
Drain potatoes and rinse under cold water.
Add celery,radishes,cucumber and onion to mayonnaise mixture - toss. Add potatoes, toss gently. Season with salt and pepper to taste. Smooth slightly across top;add sliced eggs across top of potato salad. Sprinkle a dusting of Paprika over top. Chill and serve. Any left overs can be stored chilled in a closed container for 3-4 days. It never last that long, storing is my least concern.