{"status": "success", "data": {"description_md": "Tommy and Frances are playing a game with darts and a toy clock. Frances spins the two hands on the clock, and the hands land at a random angle from the center of the circle.\n\nTommy, blindfolded, throws a dart at the clock. If the dart lands at a random location on the clock, let the probability that the dart is in the smaller angle formed by the two hands be $\\tfrac{a}{b}$ where $\\gcd(a,b)=1$. Find $100a+b$.", "description_html": "<p>Tommy and Frances are playing a game with darts and a toy clock. Frances spins the two hands on the clock, and the hands land at a random angle from the center of the circle.</p>&#10;<p>Tommy, blindfolded, throws a dart at the clock. If the dart lands at a random location on the clock, let the probability that the dart is in the smaller angle formed by the two hands be <span class=\"katex--inline\">\\tfrac{a}{b}</span> where <span class=\"katex--inline\">\\gcd(a,b)=1</span>. Find <span class=\"katex--inline\">100a+b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Christmas Contest - Team Round - Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/christmas1_team-p11", "prev": "/problem/christmas1_team-p09"}}