Triangular Numbers
Stack the dots: 1, 3, 6, 10, 15…
What is it?
The nth triangular number counts dots in a triangle with n dots per side: 1, 3, 6, 10, 15, 21… It equals n(n+1)/2 — the handshake number, the bowling-pin number, the sum of the first n counting numbers.
- Exact matches1,414
- Odds1 in 707
- Out of1,000,001
How it scores
About 1,414 triangular numbers fit in the range — roughly as rare as perfect squares — so the trait earns around ten bits on its own.
The formula: -log2(count / 1,000,001) bits per trait, capped at 20, summed with 0.5 decay per additional trait.
Highest-scoring triangular numbers
- 0score 32.6 · Mythic
- 1score 31.3 · Mythic
- 666score 31.2 · Mythic
- 55score 26.3 · Mythic
- 3score 25.1 · Mythic
- 210score 25.1 · Mythic
- 21score 25.0 · Mythic
- 10score 23.2 · Mythic
- 66score 22.4 · Mythic
- 300score 21.2 · Mythic
Related patterns
FAQ
Why are they called triangular?
Because that many dots can be arranged into an equilateral triangle — four bowling pins are 10, the fourth triangular number.
What is the largest triangular number in the game?
998,991 — that is 1413 × 1414 ÷ 2. The next one, 1,000,405, falls just outside the range.
Is every perfect square triangular?
No, but some numbers are both — 1 and 36 are square triangular numbers, and they score both traits.