MONTPELIER — Mistakes were made, but as hearings on reappraisal-related appeals moved ahead Thursday night, the Board of Civil Authority was at a loss to determine who had made them.

While one board member described the evening’s challenge as “mind-boggling” mathematics, the exercise had board members yearning for a run-of-the-mill property tax appeal — the kind where the condition of a home, the quality of its construction, the character of its neighborhood, and comparable sales can all be considered in determining its worth.