F# solution to "Escape from Zurg" puzzle - f#

Question

I have written an F# program to solve the "Escape from Zurg" puzzle
My code is the following. but somehow something is wrong with the way I am returning the boolean value when the puzzle is solved.
On the line
retVal = Move (cost + (MoveCost toy1 toy2)) Right remainingElements
I get a warning
The expression should have type 'unit' but has type 'bool'. If assigning a property use the syntax 'obj.Prop <- expr'
and I see that even though the function returns true when the puzzle is soved. when it returns the retVal remains false.
Below is my code.
open System
type Direction =
| Left
| Right
type Toy = {Name: string; Cost: int}
let toys = [
{Name="Buzz"; Cost=5};
{Name="Woody"; Cost=10};
{Name="Rex"; Cost=20};
{Name="Hamm"; Cost=25};
]
let MoveCost toy1 toy2 =
if (toy1.Cost > toy2.Cost) then
toy1.Cost
else
toy2.Cost
let rec Move cost direction group =
match group with
| [] -> if (cost > 60) then
false
else
Console.WriteLine("Solution Found!")
true
| _ ->
match direction with
| Left ->
let retVal = false
let combinations = Set.ofSeq (seq {for i in group do for j in group do if i <> j then if i < j then yield i, j else yield j, i})
for pair in combinations do
let (toy1, toy2) = pair
let remainingElements = List.filter (fun t-> t.Name <> toy1.Name && t.Name <> toy2.Name) group
retVal = Move (cost + (MoveCost toy1 toy2)) Right remainingElements
if (retVal) then
Console.WriteLine ("Move " + toy1.Name + " and " + toy2.Name + " with the total cost of " + cost.ToString())
retVal
| Right ->
let retVal = false
let toysOnRightBank = List.filter (fun t-> not(List.exists (fun g-> g = t) group)) toys
for toy in toysOnRightBank do
let cost = cost + toy.Cost
let retVal = Move cost Left (toy :: group)
if (retVal) then
Console.WriteLine("Move " + toy.Name + " back with the cost of " + toy.Cost.ToString())
retVal
[<EntryPoint>]
let main args =
let x = Move 0 Left toys
0

Answer 1

You cann't reassign a let binding. It should be:
let mutable retVal = false
...
retVal <- Move (cost + (MoveCost toy1 toy2)) Right remainingElements
However, you could easily rewrite it so that mutable isn't needed:
let res =
[
for i in group do
for j in group do
if i < j then yield i, j elif i > j then yield j, i
]
|> List.filter (fun (toy1, toy2) ->
let remainingElements = List.filter (fun t-> t.Name <> toy1.Name && t.Name <> toy2.Name) group
Move (cost + (MoveCost toy1 toy2)) Right remainingElements)
match res with
| [] -> false
| _ ->
res |> List.iter (fun (toy1, toy2) ->
Console.WriteLine ("Move " + toy1.Name + " and " + toy2.Name + " with the total cost of " + cost.ToString()))
true
EDIT: I posted a complete solution on gist, if you need a reference implementation.