I notice that some states in USA are perfectly rectangular, like the state of Colorado. I don't know if there are such states or countries elsewhere in the world.
But actually there is such! Or if I dreamt it all up, I don't know, but there is. I call the country United States of Squares, or USS for short.
This country is rectangular in its shape, and moreover it is a federation of states where all states are perfect squares. (!) All of the states is also an integer multiple of a mile. (I don't know how much a mile is in this country, but it is not very long, you don't have to take the sphereness of the Earth into account, I don't even know if USS can be found on Earth, perhaps on another hypothetical Planet of some kind.)
In this country there are 9 states, for simplicity I call them One-state, Four-state, Seven-state, Eight-state, Nine-state, Ten-state, Fourteen-state, Fifteen-state, and Eighteen-state. Their shape is squared with their respective sides 1, 4, 7, 8, 9, 10, 14, 15, an 18 miles respectively.
Your problem is to draw a map of this rectangular nation. If you can present the solution as a map, you are good.
For me to know that you have the map right, please present the states that have mutual borders with One-state.
If I am blurry somewhere, please ask me so I can rephrase or explain.
If you have a solution, please mail me your answer in order not to spoil the fun for the others. I will present who was first after a while.