A group of six imperialists Alpha, Omega, Beta, Theta, Phi and Delta carve out a circle in Antartica and break it up into six sectors. There are 48 Gold mines spread across this circle that covers an area of 3600 sq kms. Beta and Phi got the same area, while Theta and Delta got the same area. Area of Beta, Delta and Omega form an Arithmetic Progression with Delta being the middle term. Areas of Omega, Beta and Alpha form a Geometrics Progression with Beta being the middle term. The number of goldmines of Delta, Omega, Beta, Alpha and Theta form an Arithmetic Progression in that order. As many Countries have got more goldmines than Phi as have got fewer goldmines than Phi. One has to cross at least two other Countries to go from Alpha to Delta; there is only one Country to cross between Phi and Omega; and Alpha and Beta are neighboring Countries. The Country that has got the maximum number of goldmines has an area of 450 sq kms, the Country that has got the maximum area has got 6 gold mines. Omega has lesser area than his neighbor Beta and Phi has got more goldmines than his neighbor Theta.
What is the area taken up by Omega in sq kms?
How many mines did Theta take up?
Which imperialist got the least area?
Which imperialist got the region between Phi and Omega?
How many more sq kms has Alpha got than has Beta?