There are lots of very similar flags in the world, particularly the ones that are composed of three horizontal or three vertical bars. If we restrict ourselves to flags of one of these types, what is the longest path we can make by changing only one color at a time?
Q1: What is the longest path of flags composed of three horizontal bars?
Q2: What is the longest path of flags composed of three vertical bars?
Specification of rules:
- A path of length $n$ consists of flags $F_1, \ldots, F_n$
- Two flags are considered the same, if the colors of the corresponding bars only differ in shade and /or intensity.
- No path may visit the same flag twice: $F_i \ne F_j$ whenever $i \ne j$
- Neighboring flags in the path (flags $F_i$ and $F_{i+1}$) must differ in the color of exactly one bar.
- Only flags of independent countries may show up in the path.