Below is a map of a circular road. The distance between the dots is 1 kilometre. There are two houses on the road, and two more house are going to built. The local council has asked you where they should be put so that given any of the distances from 1 to 12, there are two houses that are that far apart. Of course, the two houses that are there are separated by 1 kilometre or 12 kilometres, depending upon what direction you travel, so you only have to concern yourself with the distances of 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11.
This puzzle is inspired by The six cottages from Dudeney's 536 puzzles and curious problems.