feat: OpenRouter support + 7 new AIMO3 hard problems

models.json

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+[
+  {
+    "name": "Qwen3.5-35B-A3B-Q4",
+    "url": "http://localhost:8080",
+    "api_key_env": null
+  },
+  {
+    "name": "gemini-3.1-flash-lite-preview",
+    "url": "gemini://gemini-3.1-flash-lite-preview",
+    "api_key_env": "GEMINI_API_KEY"
+  },
+  {
+    "name": "openai/gpt-oss-120b",
+    "url": "openrouter://openai/gpt-oss-120b:free",
+    "api_key_env": "OPENROUTER_API_KEY"
+  },
+  {
+    "name": "openai/gpt-oss-20b",
+    "url": "openrouter://openai/gpt-oss-20b:free",
+    "api_key_env": "OPENROUTER_API_KEY"
+  },
+  {
+    "name": "nvidia/nemotron-3-super-120b",
+    "url": "openrouter://nvidia/nemotron-3-super-120b-a12b:free",
+    "api_key_env": "OPENROUTER_API_KEY"
+  },
+  {
+    "name": "qwen/qwen3-next-80b",
+    "url": "openrouter://qwen/qwen3-next-80b-a3b-instruct:free",
+    "api_key_env": "OPENROUTER_API_KEY"
+  }
+]

problems/aimo3_hard_00eaa992.json

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+{
+  "problem_id": "aimo3_hard_00eaa992",
+  "problem_text": "If \\((60-a)(60-b)(60-c)(60-d)(60-e) = 1025\\), what is the value of \\(a + b + c + d\\)?\n\nNote: 1025 is divisible by 5.",
+  "ground_truth": "188",
+  "topic": "number_theory",
+  "source": "aimo3_hard",
+  "gptoss_20b_pass_rate": 0.125,
+  "gptoss_20b_n_correct": 2,
+  "gptoss_20b_correct_token_avg": null
+}

problems/aimo3_hard_2e0b7ba3.json

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+{
+  "problem_id": "aimo3_hard_2e0b7ba3",
+  "problem_text": "How many ways are there to paint the first level of the Th\u00e1p R\u00f9a tower model, given that the $3$ doorways at the front are painted with the same color and each of the remaining $7$ doorways is painted with one of the three colors such that any two adjacent doorways with a common side on the same level are painted with different colors?",
+  "ground_truth": "216",
+  "topic": "combinatorics",
+  "source": "aimo3_hard",
+  "gptoss_20b_pass_rate": 0.125,
+  "gptoss_20b_n_correct": 2,
+  "gptoss_20b_correct_token_avg": null
+}

problems/aimo3_hard_5f9595ae.json

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+{
+  "problem_id": "aimo3_hard_5f9595ae",
+  "problem_text": "In an acute triangle \\(ABC\\) with \\(\\angle A = 30^\\circ\\), a circle with diameter \\(BC\\) intersects \\(AB\\) and \\(AC\\) at points \\(D\\) and \\(E\\), respectively. Find the ratio of the area of \\(\\triangle ADC\\) to the area of quadrilateral \\(DBCE\\).",
+  "ground_truth": "3",
+  "topic": "geometry",
+  "source": "aimo3_hard",
+  "gptoss_20b_pass_rate": 0.125,
+  "gptoss_20b_n_correct": 2,
+  "gptoss_20b_correct_token_avg": null
+}

problems/aimo3_hard_858cba58.json

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+{
+  "problem_id": "aimo3_hard_858cba58",
+  "problem_text": "All vertices of a pyramid lie on the facets of a cube but not on its edges, and each facet contains at least one vertex. What is the maximum possible number of the vertices of the pyramid?",
+  "ground_truth": "13",
+  "topic": "other",
+  "source": "aimo3_hard",
+  "gptoss_20b_pass_rate": 0.125,
+  "gptoss_20b_n_correct": 2,
+  "gptoss_20b_correct_token_avg": null
+}

problems/aimo3_hard_b0dc264b.json

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+{
+  "problem_id": "aimo3_hard_b0dc264b",
+  "problem_text": "Given the group $(G, *)$ with $G = \\{a, b, c, d, f, g, h, k\\}$ and identity $k$, and the following operations:\n- $a * b = c$\n- $b * a = d$\n- $f * f = a$\n- $g * g = b$\n- $h * h = c$\n\nHow many self-inverses does $(G, *)$ have?",
+  "ground_truth": "2",
+  "topic": "other",
+  "source": "aimo3_hard",
+  "gptoss_20b_pass_rate": 0.125,
+  "gptoss_20b_n_correct": 2,
+  "gptoss_20b_correct_token_avg": null
+}

problems/aimo3_hard_b1da52fa.json

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+{
+  "problem_id": "aimo3_hard_b1da52fa",
+  "problem_text": "Drunk and Horse play a game on a $2023! \\times 2023!$ grid. Horse chooses a positive integer $k < 2023$ and lights up each square using $k$ different colors. Horse starts on a random square, and Drunk starts on another square exactly $2023^2$ squares away in one direction. In each turn, Drunk moves one square in some direction but cannot move in the same direction for 2023 consecutive moves. Horse moves up to $m$ squares in a direction of its choice, where $m = 2023 - k$. Horse gets alerted of the color of the square Drunk was previously on. Horse wins if it ends up on a square that shares at least one vertex with Drunk's square. What is the minimum number of turns in which Horse can guarantee a win?",
+  "ground_truth": "2030",
+  "topic": "combinatorics",
+  "source": "aimo3_hard",
+  "gptoss_20b_pass_rate": 0.125,
+  "gptoss_20b_n_correct": 2,
+  "gptoss_20b_correct_token_avg": null
+}

problems/aimo3_hard_f728b4b1.json

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+{
+  "problem_id": "aimo3_hard_f728b4b1",
+  "problem_text": "Triangle $ABC$ is constructed such that $AB>BC>AC$. Points $E$, $F$, and $G$ are drawn from $A$, $B$, and $C$ to their opposite sides respectively. If $\\frac{BE}{EC} = \\frac{7}{12}$, the ratio of $\\frac{AF}{FC}$ can be represented as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is the smallest possible sum of $m+n$?",
+  "ground_truth": "26",
+  "topic": "geometry",
+  "source": "aimo3_hard",
+  "gptoss_20b_pass_rate": 0.125,
+  "gptoss_20b_n_correct": 2,
+  "gptoss_20b_correct_token_avg": null
+}