Radish-Cucumber Salad

6 large red radishes
6 small white radishes
6 small purple radishes
1 tbsp oil
1 tsp salt
1 medium sized cucumber
1/4 tbsp fresh or 1 tsp dried tarragon
2 tsp sugar
1/8 tsp ground pepper

Trim off stem and root ends from all radishes and discard. Rinse radishes with cold water and pat dry. Cut red radishes crosswise into 3/16 inch thick slices. Stack slices, 3 or 4 at a time and cut them across into matchsticks. Place radishes in small bowl; sprinkle with 1/2 tsp salt. Toss to distribute salt and set aside at least 15 minutes to extract the radish liquid.
Cut white and purple radishes across into 1/8 inch thick slices. Place each in separate small bowls or cups. Sprinkle each with 1/4 tsp salt, toss to distribute salt and set aside.
Peel and cut cucumber, crosswise into 3/16 inch slices. In large bowl, combine cucumber, vinegar, tarragon, oil, sugar, and pepper. Toss until well-mixed, set aside.
Rinse each bowl of radishes with cold water and drain radishes in strainer. Add drained radishes to cucumber mixture. Toss until well-mixed and serve.
*Substitute 3 tbsp of distilled white viengar plus 1 tbsp water for the less pungent rice vinegar.