House of Gloom Hint #1

One way to proceed when you get stuck with a problem, is to look at simpler problems that are related.

Convince yourself that at most one firefly is required to totally illuminate houses with 3, 4, and 5 walls:


Find an example for a 6 walled house that requires 2 fireflies.

Next try to find a 9 walled house that requires 3 fireflies.

Now go back and try to find a 12 walled house that requires 4 fireflies.

You might even find a pattern for a 3N walled house requiring N fireflies.

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