The magic formula explained simply
Looking for an elegant shortcut? For a large triangle divided into n segments arranged by lines parallel to the base (here n = 4), we can use the following formula:
T(n) = n × (n + 2) × (2n + 1) ÷ 8
This result corresponds perfectly to our step-by-step counting. The beauty of this formula is that it “counts” all possible dimensions, including multilevel combinations. Ideal for testing your intuition… or for silencing a heated debate!
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