puzzle make the longest connetion u have to connet the last letter of a state with the begging of a another st

Question

make the longest connetion of the 50 states connet the last letter of one state to the first letter of another state

Answer 1

(13)
Utah - Hawaii - Idaho - Ohio - Oregon - New York - Kansas - South Dakota - Alabama - Alaska - Arizona - Arkansas - South Carolina

I don't think you can beat 13 and here's the reasoning why:

[BEGINNING] Here are states which can only occur at the beginning, noting that no states ends with C,F,L,M,P,U,V,W :
C->O Colorado /
*->N Michigan / Washington
*->A California / Florida / Louisiana / Minnesota/ Montana Pennsylvania / Virginia / West Virginia / Wisconsin
M->S Massachusetts
M->I Mississippi/ Missouri
W->A Wyoming - Georgia (2)
U->O Utah - Hawaii -> Idaho (3)
I->S Illinois S->A South Carolina

[ENDING] Here are states which can only occur at the ending, noting no state begins with E or Y and only 1 begin with D or T
*->E New Hampshire / Maine / Tennessee /
(2) Rhode Island /Maryland - Delaware
*->Y Kentucky / New Jersey
Connecticut / Vermont -> Texas (but no state ends in C or V)

[MIDDLE] As to the middle, note that far more states end in A than start with A, and only one that starts with A gets you back out of A (Arkansas), so at some point you will have to do *-> Arizona -> Alabama -> Alaska - > Arkansas

Note also there are way too many states that get you into ->A:
I->A Indiana OR I->A Iowa
N->A Nebraska OR N->A Nevada OR N->A North Carolina OR N->A North Dakota
O->A Oklahoma

Note also that the only path from N not going to A must go -> S: New York - Kansas

Note also that O must lead -> N
Ohio-> Oregon (we reject Oklahoma because we already know we have a deficit of A's)

So the rest is just chaining permutations of A,I,N,O,S for maximum length.
Might as well end with an A (South Carolina)

Answer 2

Washington, New Mexico, Oregan, North Carolina, Alabama, Arizona, Alaska, Arkansas, South Carolina,

Answer 3

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Answer 4

(12)
Michigan
New Mexico
Ohio
Oregon
New York
Kansas
South Carolina
Alabama
Alaska
Arizona
Arkansas
South Dakota