{"record":{"id":"df3ff40432b5ca67","repo":"TheAlgorithms/Python","slug":"magic-gon-side-gon-ring-is-impossible","errorCode":null,"errorMessage":"Magic {gon_side}-gon ring is impossible","messagePattern":"Magic (.+?)-gon ring is impossible","errorType":"exception","errorClass":"ValueError","httpStatus":null,"severity":"error","filePath":"project_euler/problem_068/sol1.py","lineNumber":77,"sourceCode":"    >>> solution(6)\n    Traceback (most recent call last):\n    ValueError: gon_side must be in the range [3, 5]\n    \"\"\"\n    if gon_side < 3 or gon_side > 5:\n        raise ValueError(\"gon_side must be in the range [3, 5]\")\n\n    # Since it's 16, we know 10 is on the outer ring\n    # Put the big numbers at the end so that they are never the first number\n    small_numbers = list(range(gon_side + 1, 0, -1))\n    big_numbers = list(range(gon_side + 2, gon_side * 2 + 1))\n\n    for perm in permutations(small_numbers + big_numbers):\n        numbers = generate_gon_ring(gon_side, list(perm))\n        if is_magic_gon(numbers):\n            return int(\"\".join(str(n) for n in numbers))\n\n    msg = f\"Magic {gon_side}-gon ring is impossible\"\n    raise ValueError(msg)\n\n\ndef generate_gon_ring(gon_side: int, perm: list[int]) -> list[int]:\n    \"\"\"\n    Generate a gon_side-gon ring from a permutation state\n    The permutation state is the ring, but every duplicate is removed\n\n    >>> generate_gon_ring(3, [4, 2, 3, 5, 1, 6])\n    [4, 2, 3, 5, 3, 1, 6, 1, 2]\n    >>> generate_gon_ring(5, [6, 5, 4, 3, 2, 1, 7, 8, 9, 10])\n    [6, 5, 4, 3, 4, 2, 1, 2, 7, 8, 7, 9, 10, 9, 5]\n    \"\"\"\n    result = [0] * (gon_side * 3)\n    result[0:3] = perm[0:3]\n    perm.append(perm[1])\n\n    magic_number = 1 if gon_side < 5 else 2\n","sourceCodeStart":59,"sourceCodeEnd":95,"githubUrl":"https://github.com/TheAlgorithms/Python/blob/f5988cc09713315817df6a7e327e258013a94440/project_euler/problem_068/sol1.py#L59-L95","documentation":"Raised by solution() in project_euler/problem_068/sol1.py when no permutation of the 2*gon_side numbers forms a magic gon ring. For the supported range [3, 5] magic rings are known to exist, so this branch is effectively a defensive assertion: reaching it means the permutation logic or is_magic_gon was changed/broken, not that the input is bad.","triggerScenarios":"Practically unreachable via public input since gon_side is already constrained to [3, 5] and solutions exist for all three. It can fire if someone modifies generate_gon_ring or is_magic_gon, or relaxes the range guard without checking existence.","commonSituations":"Contributors editing the permutation order or ring-sum logic during refactors; local experiments that reorder big/small number lists; regression testing after touching is_magic_gon.","solutions":["Restore the original generate_gon_ring/is_magic_gon logic if you edited them (check git diff).","Verify with the doctests: python -m doctest project_euler/problem_068/sol1.py -v.","Keep gon_side within [3, 5]; the error is a canary for internal logic bugs, not bad user input."],"exampleFix":null,"handlingStrategy":"try-catch","validationCode":null,"typeGuard":null,"tryCatchPattern":"try:\n    answer = solution(gon_side)\nexcept ValueError as e:\n    if \"impossible\" in str(e):\n        # internal invariant broke: logic was modified\n        logger.exception(\"gon search exhausted; check recent edits\")\n        raise\n    raise","preventionTips":["Run the module doctests after touching generate_gon_ring or is_magic_gon.","Treat this error as a regression signal, not an input problem.","Keep gon_side in [3, 5]; existence is guaranteed only there."],"tags":["project-euler","assertion","valueerror","internal-invariant"],"backgroundTag":null,"analyzedSha":"f5988cc09713315817df6a7e327e258013a94440","analyzedAt":"2026-08-14T17:30:07.041Z","schemaVersion":2},"datasetVersion":"2026-08-15T17:31:12.345Z"}