Can You Crack And Pack Riddler Nation?

Riddler Classic

From Ivor Traber comes a division of the Lower 48:

Previously on The Riddler, you were tasked with splitting the contiguous United States into two groups of states, themselves contiguous, that were approximately equal in area. This week’s Classic is similar.

The states of California, Colorado, New Mexico and New York have banded together to form the United States of Yellow (USY). Meanwhile, Florida, Texas, Utah and Wyoming are the first states to join the United States of Purple (USP). The remaining 40 contiguous states join either the USY or the USP, such that both new nations have 24 states and these sets of states are themselves contiguous.

Virginia is leaning toward joining the United States of Yellow. Is there any way for it to do this?

(Note: For the purposes of this riddle, Colorado does not border Arizona, and Utah does not border New Mexico. Also, Michigan’s two peninsulas can be thought of as connected, so that Michigan borders Ohio, Indiana and Wisconsin.)

Solution

Northeast

Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, and Vermont must be part of the USY, as New York prevents them from being contiguous with USP.

Arizona

California cannot be contiguous to the rest of USY via Montana, South Dakota, and Nebraska. That would prevent Wyoming and Utah from being contiguous with Texas and the rest of USP.

Arizona must be part of the USY.

USY

Washington, Oregon, Idaho, Montana, North Dakota, Minnesota, Wisconsin, Michigan, Ohio, and Pennsylvania must be a part of USY in order to be contiguous with New York.

That means 21 states are currently in the USY

Answer

If Virginia is in the USY, New Jersey, Delaware, and Maryland must be as well, which yields 25 states in the USY.

Virginia cannot be part of the USY with the given founding members of the USY and USP and both groups be contiguous and have 24 each.

I created an interactive to visualize the solution, but I do not think it is possible.

Rohan Lewis

2022.07.11

Code can be found here.