Hat Check Problem Calculator

P(match) → 1 − 1/e

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n hats (1–15)

P(≥1 match)

63.2121%

1−1/e limit

63.2121%

!10 = 1,334,961E[matches]=1

Convergence to 1−1/e

n=1100.0000%

n=250.0000%

n=366.6667%

n=462.5000%

n=563.3333%

n=663.1944%

n=763.2143%

n=863.2118%

n=963.2121%

n=1063.2121%

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About Hat Check Problem Calculator

A hat check problem calculator exploring the classic probability puzzle: n hats randomly returned, what's P(at least one match)? Answer: 1-1/e ≈ 63.2% as n→∞. Uses derangement count !n = n!·Σ(-1)^k/k!. Related to inclusion-exclusion principle. Client-side.

Hat Check Problem Calculator Features

P(≥1 match)
P(exactly k)
Derangement count
1/e convergence
Expected matches

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