Consider a triangular grid made of matchsticks. Three matches are needed to
make a single triangle. To break it, you can remove any single match.
Nine matches are needed to make a length 2 grid of
triangles (6 for the perimeter and 3 internal.)
There are 5 triangles in such a grid,
four of size 1 and one of size 2. To eliminate all triangles,
three matches must be removed
(an external match must be removed to break the size 2 triangle,
but this leaves three size 1 triangles, and at least two more
matches must be removed to leave no full triangles.)
/ \
---
/ \ / \
--- ---
/ \ / \ / \
--- --- ---
What is the fewest number of matches which must be removed to break all
triangles - of any size - in:
a size 3 grid (originally 18 matches, as shown)?
a size 4 grid (originally 30 matches)?
a size 5 grid (originally 45 matches)?
Source: Original extension of previous Vanishing Squares puzzle.
Solution
Mail to Ken