  In the mysterious and colorful world of chromatic numbers, where there are a
lot of unknown, there is an amazing thing. It turns out that for some intervals
of forbidden distances on the plane, one can specify the exact value of the
chromatic number $\chi$. Two sets of such intervals have been found, for
$\chi=7$ and 9. We call them islands of certainty. Here we increase the size of
these islands, and add three new ones with $\chi=8$, 12, 13. We also %formulate
conjectures which predict conjecture islands for $\chi=14$, 15, 16. Are there
islands of certainty for $\chi$=10 or 11? This is still a mystery. Roll up for
the Mystery Tour.
