Ménage Number Calculator
Count reduced circular ménage arrangements with one sex fixed in circular order and opposite-sex placements avoiding adjacent spouses; n≥2, no extra rotation/sex arrangement multiplier.
Description
Reduced circular ménage counting fixes one group's circular order and avoids spouse adjacency in placements of the other group.
Reduced circular ménage counting fixes one group's circular order and avoids spouse adjacency in placements of the other group. Rotation and extra seating-order multipliers depend on the chosen counting convention.1
Count reduced circular ménage arrangements with one sex fixed in circular order and opposite-sex placements avoiding adjacent spouses; n≥2, no extra rotation/sex arrangement multiplier.
When to use Ménage Number Calculator
Use this tool to count reduced circular ménage arrangements with one sex fixed in circular order and opposite-sex placements avoiding adjacent spouses; n≥2, no extra rotation/sex arrangement multiplier.
Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
How to use Ménage Number Calculator and understand its results
- Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
- Enter coupleCount using the field table and calculation rules, then run the tool.
- Read exactMenageArrangementCount. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| coupleCount | Couple count | number | Required |
Enter integer couple count from 2 to 64. Evaluate the exact inclusion-exclusion expression using BigInt factorials and binomial coefficients; return the decimal integer string.
count = Σ[k=0..n](−1)^k [2n/(2n−k)] C(2n−k,k)(n−k)!, n≥2 Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| exactMenageArrangementCount | Exact menage arrangement count | string |
{
"input": {
"coupleCount": 3
},
"output": {
"exactMenageArrangementCount": "1"
}
}Limitations and assumptions
This is the reduced fixed-order convention. Do not add rotation or group-order factors unless the intended seating problem requires them.
Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Factorial Digit Count Calculator: Count exact radix digits of n! using bounded BigInt factorial, avoiding logarithm rounding at powers of base; 0!=1 has one digit. For a complementary task, use Bell Transform Calculator: Compute complete exponential Bell-polynomial transform with b0=1 and b_n=Σ C(n−1,k−1)a_k b_(n−k); caller sequence differs materially from a single Bell number.
References
-
Ménage Number Calculator — tool.io
Similar or alternative tools
- Factorial Digit Count Calculator
Count exact radix digits of n! using bounded BigInt factorial, avoiding logarithm rounding at powers of base; 0!=1 has one digit.
- Bell Transform Calculator
Compute complete exponential Bell-polynomial transform with b0=1 and b_n=Σ C(n−1,k−1)a_k b_(n−k); caller sequence differs materially from a single Bell number.