in case you're planning a road trip

Suppose you want to plan a road trip around this great country of ours.

Now, you want to visit all 48 contiguous states. But you're kind of anal retentive. So you want a path that will take you through all 48 without returning to any state once you've left it. The following is true:

• Your path will either start in Maine or end in Maine;
• If your path starts in Maine, the first seven states you visit will be (in order): Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut, New York;
• If your path ends in Maine, the last seven states you visit will be (in order): New York, Connecticut, Rhode Island, Massachusetts, Vermont, New Hampshire, Maine.

The proof is left to the reader.