On a board there are
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
nails, each two connected by a rope. Each rope is colored in one of
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
given distinct colors. For each three distinct colors, there exist three nails connected with ropes of these three colors.
a) Can
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
be
![6](/media/m/e/e/e/eeec330d59a70f8ed1d6882474cb02a3.png)
?
b) Can
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
be
![7](/media/m/5/1/9/519154d5119d15088eebb25b656d58dd.png)
?
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On a board there are $n$ nails, each two connected by a rope. Each rope is colored in one of $n$ given distinct colors. For each three distinct colors, there exist three nails connected with ropes of these three colors.
a) Can $n$ be $6$ ?
b) Can $n$ be $7$ ?