Fix #194: define R in problem 101 statement and fix its sample

[whuang369]

R is the upper bound on the number of OR gates in the hidden circuit (the interactor rejects inputs with more than R '|'), but the statement called it "R external switches" and never said what it bounds. Without the bound the problem is unsolvable within the query limit: an arbitrary T for N = 8000 needs 8000 bits, while log2 C(8000, 120) ~ 894 matches the 900-query full-score threshold.

The sample was also invalid: its wiring broke i < Ui < Vi and the "exactly one" rule, and its queries had length 5 instead of 2N+1 = 7 (the interactor answers Wrong Answer [4]). Replace it with a valid wiring; the two replies and the final accept were checked against interactor.cpp.

Summary

Please read CONTRIBUTING.md before submitting.

Type of Change

• New research problem
• New algorithmic problem
• New Frontier-CS 2.0 problem
• Bug fix
• Documentation update
• Other:

Testing

Checklist

• Code follows the project structure and conventions
• Self-review completed
• Documentation updated (if applicable)

CI Validation (for new problems)

When adding new problems, CI will automatically validate that your reference solution achieves score > 0.

• Algorithmic problems: Include reference.cpp in your problem directory
• Research problems: Include reference.py (or reference.cpp if language: cpp in config.yaml)
• 2.0 problems: Include reference.py unless the problem config declares another language