Solves the "Two Logicians" puzzle.
Posted by Vandroiy
// Two perfect logicians, S and P, are told that integers x and y have been chosen // such that 1 < x < y and x+y < 100. S is given the value x+y and P is given the // value xy. They then have the following conversation. // // P: I cannot determine the two numbers. // S: I knew that. // P: Now I can determine them. // S: So can I. // // Given that the above statements are true, what are the two numbers? let inOp op f = Seq.groupBy ((<||) op) >> Seq.map snd >> Seq.filter f >> Seq.concat let singleCase op = inOp op (Seq.length >> (=) 1) let all = [for x = 2 to 49 do for y = x + 1 to 99 - x do yield x, y] let spoilP = all |> singleCase (*) |> set all |> inOp (+) (set >> Set.intersect spoilP >> Set.isEmpty) |> singleCase (*) |> singleCase (+) |> Seq.exactlyOne