{
  "benchmark": "postcutoff_pilot_v1",
  "freeze_tag": "postcutoff-pilot-v1-freeze-20260705",
  "dataset_sha256": "b5ef06357d5c0077ed5dbf35508eeee46a73dfb22dbcc81f7510989601ca4595",
  "task_count": 5,
  "tasks": [
    {
      "task_id": "PILOT-N2",
      "task_type": "math",
      "problem": "A 3 x 10 rectangle is to be tiled completely, with no overlaps and nothing extending outside the rectangle, using exactly two 1 x 1 square tiles and exactly fourteen 1 x 2 domino tiles. Dominoes may be placed horizontally or vertically, and tiles of the same shape are indistinguishable. Two tilings are different if some cell of the rectangle is covered differently. Find the number of such tilings."
    },
    {
      "task_id": "PILOT-K1",
      "task_type": "code",
      "problem": "Define a sequence by s(1) = 2026 and, for every integer n >= 2, s(n) = s(n-1) + M(s(n-1)) * d(n), where M(k) denotes the largest decimal digit of k and d(n) denotes the number of positive divisors of n. Find s(2026)."
    },
    {
      "task_id": "PILOT-Q1",
      "task_type": "simple_qa",
      "problem": "A regional depot operates Monday through Friday. On Monday it ships 48 crates, and on each later day it ships 6 more crates than on the previous day. Every crate holds 36 units, except that on Wednesday exactly one third of that day's crates are shipped half-full with 18 units each. Of the crates shipped on Friday, 8 are returned unopened, and their contents do not count toward the week's deliveries. How many units does the depot deliver for the week in total?"
    },
    {
      "task_id": "PILOT-R1",
      "task_type": "reasoning",
      "problem": "Ava, Ben, Cleo, Dan, and Eve finished a race in positions 1 through 5, with no ties. Exactly two of the five always lie and the other three always tell the truth, and the two liars finished in consecutive positions. It is also known that Ava finished ahead of Dan. Ava says: I finished immediately ahead of Ben. Ben says: Cleo finished last. Cleo says: I finished ahead of Ava. Dan says: Eve did not finish first. Eve says: Dan finished third. Find the product of the positions in which the two liars finished."
    },
    {
      "task_id": "PILOT-C1",
      "task_type": "code",
      "problem": "Find every integer n with 2 <= n <= 300000 such that n, n + 4, and n + 6 are all prime. List all such n in increasing order. Then let A be the number of such n and B be the largest such n. Report A + B as your final answer."
    }
  ]
}