A map maker is making a map which will include the following five states: Texas, Oklahoma, Louisiana, Mississippi, & Arkansas. The map maker only has $3$ colors to use: red, green, & blue. In addition, no two two states which share a border can be colored using the same color. Your goal is to write a Prolog rule which $$nds an acceptable assignment of colors to states so that any two states that share a border do not have the same color. Write a Prolog rule states$/5$ which succeeds when an acceptable coloring is given for the states Texas, Oklahoma, Louisiana, Mississippi, and Arkansas in that order. You should not use a graph as the underlying data structure.

$?-$ states$($blue$,$ blue, red, red, green$).\%$ invalid coloring

false.

$?-$ states$($brown$,$ black, purple, navy, maroon$).\%$ invalid colors

false.

$?-$ states$($Texas$,$ Oklahoma, Louisiana, Mississippi, Arkansas$).$

Texas $=$ Mississippi, Mississippi $=$ red,

Oklahoma $=$ Louisiana, Louisiana $=$ green,

Arkansas $=$ blue $.$

$?-$ states$($blue$,$ Oklahoma, Louisiana, Mississippi, Arkansas$).$

Oklahoma $=$ Louisiana, Louisiana $=$ red,

Mississippi $=$ blue,

Arkansas $=$ green $.$