open System
let isFractional n =
n <> (Decimal.Truncate n)
let correct n =
//round after 20th digit after decimal point to fix propagation of floating point errors
Decimal.Round(n, 20)
let resultAndWhetherItHasFractionalSubResults (n : list<decimal>) =
let result = n.[0] + 13M * n.[1] / n.[2] + n.[3] + 12M * n.[4] - n.[5] - 11M + n.[6] * n.[7] / n.[8] - 10M
let hasFractionalSubResults = isFractional (correct(n.[1] / n.[2])) || isFractional (correct(n.[7] / n.[8]))
(correct result, hasFractionalSubResults) //return tuple
let ``1st solution in blog post`` = resultAndWhetherItHasFractionalSubResults ([1; 2; 6; 4; 7; 8; 3; 5; 9] |> List.map (fun n -> n |> decimal))
// source: http://stackoverflow.com/questions/286427/calculating-permutations-in-f
let rec permute list taken =
seq {
if Set.count taken = List.length list
then yield List.empty
else
for element in list do
if not (Set.contains element taken) then
for permutation in permute list (Set.add element taken) do
yield element::permutation
} |> List.ofSeq
//returns solutions as tuple in the form of ((input, (result, hasFractionalSubResults))
let solutions allowFractionalSubResults=
let numbers = [1; 2; 3; 4; 5; 6; 7; 8; 9] |> List.map (fun n -> n |> decimal)
permute numbers Set.empty
|> List.map (fun input -> (input, resultAndWhetherItHasFractionalSubResults input))
|> List.filter (fun (input, (result, hasFractionalSubResults)) -> result = 66M && (allowFractionalSubResults || (not hasFractionalSubResults)))
let ``solutions WITH fractional sub-results`` = solutions true
let ``number of solutions WITH fractional sub-results`` = ``solutions WITH fractional sub-results`` |> List.length
let ``solutions WITHOUT fractional sub-results`` = solutions false
let ``number of solutions WITHOUT fractional sub-results`` = ``solutions WITHOUT fractional sub-results`` |> List.length
(********OUTPUT*****************
...
val ( 1st solution in blog post ) : decimal * bool =
(66.00000000000000000000M, true)
...
val ( solutions WITH fractional sub-results ) :
(decimal list * (decimal * bool)) list =
[([1M; 2M; 6M; 4M; 7M; 8M; 3M; 5M; 9M], (66.00000000000000000000M, true));
([1M; 2M; 6M; 4M; 7M; 8M; 5M; 3M; 9M], (66.00000000000000000000M, true));
([1M; 3M; 2M; 4M; 5M; 8M; 7M; 9M; 6M], (66.0M, true));
([1M; 3M; 2M; 4M; 5M; 8M; 9M; 7M; 6M], (66.0M, true));
([1M; 3M; 2M; 9M; 5M; 6M; 4M; 7M; 8M], (66.0M, true));
([1M; 3M; 2M; 9M; 5M; 6M; 7M; 4M; 8M], (66.0M, true));
([1M; 3M; 4M; 7M; 6M; 5M; 2M; 9M; 8M], (66.00M, true));
([1M; 3M; 4M; 7M; 6M; 5M; 9M; 2M; 8M], (66.00M, true));
([1M; 3M; 6M; 2M; 7M; 9M; 4M; 5M; 8M], (66.0M, true));
([1M; 3M; 6M; 2M; 7M; 9M; 5M; 4M; 8M], (66.0M, true));
([1M; 3M; 9M; 4M; 7M; 8M; 2M; 5M; 6M], (66.00000000000000000000M, true));
([1M; 3M; 9M; 4M; 7M; 8M; 5M; 2M; 6M], (66.00000000000000000000M, true));
([1M; 4M; 8M; 2M; 7M; 9M; 3M; 5M; 6M], (66.0M, true));
([1M; 4M; 8M; 2M; 7M; 9M; 5M; 3M; 6M], (66.0M, true));
([1M; 5M; 2M; 3M; 4M; 8M; 7M; 9M; 6M], (66.0M, true));
([1M; 5M; 2M; 3M; 4M; 8M; 9M; 7M; 6M], (66.0M, true));
([1M; 5M; 2M; 8M; 4M; 7M; 3M; 9M; 6M], (66.0M, true));
([1M; 5M; 2M; 8M; 4M; 7M; 9M; 3M; 6M], (66.0M, true));
([1M; 5M; 3M; 9M; 4M; 2M; 7M; 8M; 6M], (66.00000000000000000000M, true));
([1M; 5M; 3M; 9M; 4M; 2M; 8M; 7M; 6M], (66.00000000000000000000M, true));
([1M; 8M; 3M; 7M; 4M; 5M; 2M; 6M; 9M], (66.00000000000000000000M, true));
([1M; 8M; 3M; 7M; 4M; 5M; 6M; 2M; 9M], (66.00000000000000000000M, true));
([1M; 9M; 6M; 4M; 5M; 8M; 3M; 7M; 2M], (66.0M, true));
([1M; 9M; 6M; 4M; 5M; 8M; 7M; 3M; 2M], (66.0M, true));
([1M; 9M; 6M; 7M; 5M; 2M; 3M; 4M; 8M], (66.0M, true));
([1M; 9M; 6M; 7M; 5M; 2M; 4M; 3M; 8M], (66.0M, true));
([2M; 1M; 4M; 3M; 7M; 9M; 5M; 6M; 8M], (66.00M, true));
([2M; 1M; 4M; 3M; 7M; 9M; 6M; 5M; 8M], (66.00M, true));
([2M; 3M; 6M; 1M; 7M; 9M; 4M; 5M; 8M], (66.0M, true));
([2M; 3M; 6M; 1M; 7M; 9M; 5M; 4M; 8M], (66.0M, true));
([2M; 4M; 8M; 1M; 7M; 9M; 3M; 5M; 6M], (66.0M, true));
([2M; 4M; 8M; 1M; 7M; 9M; 5M; 3M; 6M], (66.0M, true));
([2M; 6M; 9M; 8M; 5M; 1M; 4M; 7M; 3M], (66.00000000000000000000M, true));
([2M; 6M; 9M; 8M; 5M; 1M; 7M; 4M; 3M], (66.00000000000000000000M, true));
([2M; 8M; 6M; 9M; 4M; 1M; 5M; 7M; 3M], (66.00000000000000000000M, true));
([2M; 8M; 6M; 9M; 4M; 1M; 7M; 5M; 3M], (66.00000000000000000000M, true));
([2M; 9M; 6M; 3M; 5M; 1M; 4M; 7M; 8M], (66.0M, true));
([2M; 9M; 6M; 3M; 5M; 1M; 7M; 4M; 8M], (66.0M, true));
([3M; 1M; 4M; 2M; 7M; 9M; 5M; 6M; 8M], (66.00M, true));
([3M; 1M; 4M; 2M; 7M; 9M; 6M; 5M; 8M], (66.00M, true));
([3M; 2M; 1M; 5M; 4M; 7M; 8M; 9M; 6M], (66M, true));
([3M; 2M; 1M; 5M; 4M; 7M; 9M; 8M; 6M], (66M, true));
([3M; 2M; 4M; 8M; 5M; 1M; 7M; 9M; 6M], (66.0M, true));
([3M; 2M; 4M; 8M; 5M; 1M; 9M; 7M; 6M], (66.0M, true));
([3M; 2M; 8M; 6M; 5M; 1M; 7M; 9M; 4M], (66.00M, true));
([3M; 2M; 8M; 6M; 5M; 1M; 9M; 7M; 4M], (66.00M, true));
([3M; 5M; 2M; 1M; 4M; 8M; 7M; 9M; 6M], (66.0M, true));
([3M; 5M; 2M; 1M; 4M; 8M; 9M; 7M; 6M], (66.0M, true));
([3M; 6M; 4M; 9M; 5M; 8M; 1M; 7M; 2M], (66.0M, true));
([3M; 6M; 4M; 9M; 5M; 8M; 7M; 1M; 2M], (66.0M, true));
([3M; 9M; 2M; 8M; 1M; 5M; 6M; 7M; 4M], (66.0M, true));
([3M; 9M; 2M; 8M; 1M; 5M; 7M; 6M; 4M], (66.0M, true));
([3M; 9M; 6M; 2M; 5M; 1M; 4M; 7M; 8M], (66.0M, true));
([3M; 9M; 6M; 2M; 5M; 1M; 7M; 4M; 8M], (66.0M, true));
([4M; 2M; 6M; 1M; 7M; 8M; 3M; 5M; 9M], (66.00000000000000000000M, true));
([4M; 2M; 6M; 1M; 7M; 8M; 5M; 3M; 9M], (66.00000000000000000000M, true));
([4M; 3M; 2M; 1M; 5M; 8M; 7M; 9M; 6M], (66.0M, true));
([4M; 3M; 2M; 1M; 5M; 8M; 9M; 7M; 6M], (66.0M, true));
([4M; 3M; 9M; 1M; 7M; 8M; 2M; 5M; 6M], (66.00000000000000000000M, true));
([4M; 3M; 9M; 1M; 7M; 8M; 5M; 2M; 6M], (66.00000000000000000000M, true));
([4M; 9M; 6M; 1M; 5M; 8M; 3M; 7M; 2M], (66.0M, true));
([4M; 9M; 6M; 1M; 5M; 8M; 7M; 3M; 2M], (66.0M, true));
([5M; 1M; 2M; 9M; 6M; 7M; 3M; 4M; 8M], (66.0M, true));
([5M; 1M; 2M; 9M; 6M; 7M; 4M; 3M; 8M], (66.0M, true));
([5M; 2M; 1M; 3M; 4M; 7M; 8M; 9M; 6M], (66M, true));
([5M; 2M; 1M; 3M; 4M; 7M; 9M; 8M; 6M], (66M, true));
([5M; 3M; 1M; 7M; 2M; 6M; 8M; 9M; 4M], (66M, true));
([5M; 3M; 1M; 7M; 2M; 6M; 9M; 8M; 4M], (66M, false));
([5M; 4M; 1M; 9M; 2M; 7M; 3M; 8M; 6M], (66M, true));
([5M; 4M; 1M; 9M; 2M; 7M; 8M; 3M; 6M], (66M, true));
([5M; 4M; 8M; 9M; 6M; 7M; 1M; 3M; 2M], (66.0M, true));
([5M; 4M; 8M; 9M; 6M; 7M; 3M; 1M; 2M], (66.0M, true));
([5M; 7M; 2M; 8M; 3M; 9M; 1M; 6M; 4M], (66.0M, true));
([5M; 7M; 2M; 8M; 3M; 9M; 6M; 1M; 4M], (66.0M, true));
([5M; 9M; 3M; 6M; 2M; 1M; 7M; 8M; 4M], (66M, false));
([5M; 9M; 3M; 6M; 2M; 1M; 8M; 7M; 4M], (66M, true));
([6M; 2M; 8M; 3M; 5M; 1M; 7M; 9M; 4M], (66.00M, true));
([6M; 2M; 8M; 3M; 5M; 1M; 9M; 7M; 4M], (66.00M, true));
([6M; 3M; 1M; 9M; 2M; 5M; 7M; 8M; 4M], (66M, false));
([6M; 3M; 1M; 9M; 2M; 5M; 8M; 7M; 4M], (66M, true));
([6M; 9M; 3M; 5M; 2M; 1M; 7M; 8M; 4M], (66M, false));
([6M; 9M; 3M; 5M; 2M; 1M; 8M; 7M; 4M], (66M, true));
([7M; 1M; 4M; 9M; 6M; 5M; 2M; 3M; 8M], (66.00M, true));
([7M; 1M; 4M; 9M; 6M; 5M; 3M; 2M; 8M], (66.00M, true));
([7M; 2M; 8M; 9M; 6M; 5M; 1M; 3M; 4M], (66.00M, true));
([7M; 2M; 8M; 9M; 6M; 5M; 3M; 1M; 4M], (66.00M, true));
([7M; 3M; 1M; 5M; 2M; 6M; 8M; 9M; 4M], (66M, true));
([7M; 3M; 1M; 5M; 2M; 6M; 9M; 8M; 4M], (66M, false));
([7M; 3M; 2M; 8M; 5M; 9M; 1M; 6M; 4M], (66.0M, true));
([7M; 3M; 2M; 8M; 5M; 9M; 6M; 1M; 4M], (66.0M, true));
([7M; 3M; 4M; 1M; 6M; 5M; 2M; 9M; 8M], (66.00M, ...)); ...]
val ( number of solutions WITH fractional sub-results ) : int = 136
val ( solutions WITHOUT fractional sub-results ) :
(decimal list * (decimal * bool)) list =
[([5M; 3M; 1M; 7M; 2M; 6M; 9M; 8M; 4M], (66M, false));
([5M; 9M; 3M; 6M; 2M; 1M; 7M; 8M; 4M], (66M, false));
([6M; 3M; 1M; 9M; 2M; 5M; 7M; 8M; 4M], (66M, false));
([6M; 9M; 3M; 5M; 2M; 1M; 7M; 8M; 4M], (66M, false));
([7M; 3M; 1M; 5M; 2M; 6M; 9M; 8M; 4M], (66M, false));
([9M; 3M; 1M; 6M; 2M; 5M; 7M; 8M; 4M], (66M, false))]
val ( number of solutions WITHOUT fractional sub-results ) : int = 6
end
*)