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Description
Solution to Viral Math Problem From Vietnam explained on: http://mindyourdecisions.com/blog/2015/05/20/viral-math-problem-from-vietnam-are-you-smarter-than-an-8-year-old/#.VXhmhs-eDRY
Source code
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 *)
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