New Hampshire Route 31  New Hampshire Route 31 (abbreviated NH 31) is a north–south state highway in southern New Hampshire. It runs from Mason on the Massachusetts border to Goshen. The southern terminus of NH 31 is in Mason at the Massachusetts state line, where, as Greenville Road, the road becomes Massachusetts Route 31. The northern terminus of NH 31 is in Goshen at New Hampshire Route 10. NH 31 intersects New Hampshire Route 124 within of the Massachusetts border. It passes through Greenville, Wilton, Lyndeborough, Greenfield, Bennington, Antrim, Hillsborough, Windsor, and Washington on its way to Goshen. NH 31 runs concurrent with New Hampshire Route 9 for a distance of approximately where it passes on the west side of Franklin Pierce Lake in the town of Hillsborough. In other places, the road merges with U.S. Route 202 and New Hampshire Route 101 for a distance. Route 31 uses the following names as it passes through different towns: