Mathematics fact in AirportCity

[Dafsade]

Hi everybody !

I have realized a funny fact (funny for people who likes (loves ?) mathematics !

One 3x3 building takes exactly twice more place than one 2x2 building !

Indeed, it works only for building which requires a road.

Because 2x(2x2 + 1) = 3x3+1
=> 2 buildings 2x2 with 1 road = 1 building 3x3 with one road.

I found this fact absolutely surprising !

So, the equation to solve is 2(X.X+1) = Y.Y+1

Of course, there is an infinity of solutions.
What we are looking for is only integer solutions ! There is an infinity too, but I did a little calculation and my results is : for x (integer) from 0 to 200 000 there are only 7 Solutions (integer) !

Conclusion : we are really lucky that our case is a solution of this problem ! Because it allows us to make easy calculations. Indeed, we can say that one 3x3 building is equals to 2 2x2 buildings !

No, i am not crazy guys !

 

[exwhy]

oops, I've lost you after the equations

now.. what if we introduce a new possibility that 1 piece of road can serve 4 buildings of either size? (windmill shape.) does 3x3 building become a tiny bit more space efficient?

 

[Dafsade]

oops, I've lost you after the equations

now.. what if we introduce a new possibility that 1 piece of road can serve 4 buildings of either size? (windmill shape.) does 3x3 building become a tiny bit more space efficient?

Ah ah ah !

With this assumption, the problem is more complicated ! Without calculation I am not able to reply with accuracy !
But, I guess 3x3 buildings are always worse than 2x2 buildings !

 

[LX Air - Teresa]

Hi everybody !

I have realized a funny fact (funny for people who likes (loves ?) mathematics !

One 3x3 building takes exactly twice more place than one 2x2 building !

Indeed, it works only for building which requires a road.

Because 2x(2x2 + 1) = 3x3+1
=> 2 buildings 2x2 with 1 road = 1 building 3x3 with one road.

I found this fact absolutely surprising !

So, the equation to solve is 2(X.X+1) = Y.Y+1

Of course, there is an infinity of solutions.
What we are looking for is only integer solutions ! There is an infinity too, but I did a little calculation and my results is : for x (integer) from 0 to 200 000 there are only 7 Solutions (integer) !

Conclusion : we are really lucky that our case is a solution of this problem ! Because it allows us to make easy calculations. Indeed, we can say that one 3x3 building is equals to 2 2x2 buildings !

No, i am not crazy guys !

But you’re assuming that for each 2x2 building you must have a 1x1 road (hence x**2+1) when in fact that’s an upper bound for the real value.
Taking only into consideration the 10 small squares case, you can either use it (assuming you can shape the 10 squares as you need/want)
One 3x3 and a road
Two 2x2, one 1x1 and a road
Seven 1x1, and 3 roads
One 2x2, four 1x1 and 2 roads
And I guess that’s all, assuming all buildings need roads