Title: Fuzzy friends
Introduction
Congratulations! You've been selected to do research a a newly discovered animal called a fuzzy, a docile, simple creature that strongly resembles a cotton ball. Fuzzies love to be near other fuzzies, but not all fuzzies want to be near each other.
There are 6 ty...
Grimm's conjecture states that, for any set of consecutive composite numbers \$n+1, n+2, ..., n+k\$, there exist \$k\$ distinct primes \$p_i\$, such that \$p_i\$ divides \$n+i\$ for each \$1 \le i \le k\$.
For example, take \$\{24, 25, 26, 27, 28\}\$. We can see that if we take the primes \$2, 5,...
Imagine you have a grid where some squares are walls, some are empty, and some are lights that shine for arbitrary distances in the four cardinal directions until they meet walls:
####.####
##..L....
####.##.#
####.##L.
##......L
In the above grid, the lights cover all the tiles. But in some cas...
