Practice question · Estimate
With 40 meaningless units and words up to 5 units long, roughly how many possible word forms exist, in millions, before any constraint on legal sequences?
Estimate on a scale from 0 million (0) to 200 million (200).
Hints
- Sum the possibilities for lengths one through five.
- Forty to the fifth power alone is over a hundred million.
Show the answer
100 (answers within ±25 count)
Why
Around 100 million: forty to the fifth is 102.4 million on its own, and the shorter lengths add little. The number is absurdly larger than any vocabulary, which is the point: duality gives so much headroom that every language can afford to leave most possible forms unused.
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