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$\begingroup$ For the upper bound. It is trivial one can't fit all 15 because one can't put any additional triangle right up to the outer edges of the hexagon. One can compute a minimal unfilled triangular area in each of the 3 remaining empty corners of the hexagon. If these areas add up to more than one triangle that would show that 14 is impossible as well. $\endgroup$

quarague
– quarague

2025-06-05 13:20:48 +00:00
Commented Jun 5, 2025 at 13:20
1

$\begingroup$ I’m giving you the tick since it’s the best (and only) answer so far. I also tried beating 12 and failed. $\endgroup$

Pranay
– Pranay

2025-06-09 13:53:16 +00:00
Commented Jun 9, 2025 at 13:53

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