In detail

The impossible arithmetic

The impossible arithmetic

Find nine different integers from 1 to 20, such that no combination of three of the nine integers forms an arithmetic progression.

For example, if two of the elected members were 7 and 13, then that would prevent 1, 10, and 19 from being included.

Solution

There are two possible solutions:

  • 1, 2, 6, 7, 9, 14, 15, 18, 20
  • 1, 3, 6, 7, 12, 14, 15, 19, 20