You are a lone builder. You have to build a city on a 10x10 initial empty grid. You can place:
- a street, which is a blue cell on the top of any cell,
- a tomato shop, which is a red cell on any cell having a street in one of his 4-neighbors,
- a small house, which is a green cell on any cell having a street and a tomato shop in two of his 4-neighbors,
- a tall building, which is a yellow cell on any cell having a street, a tomato shop and a house in three of his 4-neighbors.
These rules are valid during the construction step only: if a cell is replaced by another one, it has to comply the rules, but its neighbors can break them.
Below is an example of a possible city:
The question is easy:
How many yellow tall buildings can you build in the city, and in how many steps? An answer is considered better than another one if it maximizes the number of buildings, or if the number is the same but it does it in a lower number of steps.
For instance, if you would be given a 3x3 city, you could build 4 buildings in 12 steps:
For the little story, I got inspired from a now unavailable Android game: com.amusetime.buildingtower