initial commit

33_cancelling.fs

@@ -0,0 +1,37 @@
+module _33
+
+open common
+
+let cancelling =
+    let nds = seq {
+        for d in 11..99 do
+            if d % 10 <> 0 then
+                for n in 11..(d-1) do
+                    if n % 10 <> 0 then
+                        yield (n,d)
+        }
+
+    let cancelCommonDigits (n,d) =
+        let nd = numDigits n
+        let dd = numDigits d
+        seq {
+            for ndi in nd do
+                for ddi in dd do
+                    if ndi = ddi then
+                        let ndmi = Array.filter ((<>) ndi) nd
+                        let ddmi = Array.filter ((<>) ddi) dd
+                        if (ndmi.Length > 0 && ddmi.Length > 0) then
+                            yield (digitsNum ndmi, digitsNum ddmi)
+        }
+    
+    nds
+    |> Seq.collect (fun (n,d) -> 
+        let f = float n/float d
+        cancelCommonDigits (n,d) 
+        |> Seq.map (fun (cn,cd) -> (float cn/float cd,cn,cd,n,d))
+        |> Seq.filter (fun (cf,_,_,_,_) -> cf = f)
+        )
+    |> Seq.fold (fun (pn, pd) (_,n,d,_,_) -> (pn * n, pd * d)) (1,1)
+    |> Fraction.reduce
+    |> snd
+