I was playing Dishonored II (great game, by the way), when I came across a locked door. In order to make progress in the game, I had to open this door. When you get close to it, you begin to realise that there is more to this door than it first meets the eye:

Guia circuit track layout
The Jindosh Riddle door lock

There is no key that opens this door. Instead, you have 5 slots with names and 5 slots with objects which need to have the right values to unlock the door. You don’t have to brute force the combination, though, because right next to the door you can find the following riddle:

At the dinner party were Lady Winslow, Doctor Marcolla, Countess Contee, Madam Natsiou, and Baroness Finch.

The women sat in a row. They all wore different colors and Doctor Marcolla wore a jaunty white hat. Countess Contee was at the far left, next to the guest wearing a blue jacket. The lady in green sat left of someone in red. I remember that green outfit because the woman spilled her absinthe all over it. The traveller from Dabokva was dressed entirely in purple. When one of the dinner guests bragged about her Snuff Tin, the woman next to her said they were finer in Dabokva, where she lived.

So Lady Winslow showed off a prized Diamond, at which the lady from Fraeport scoffed, saying it was no match for her War Medal. Someone else carried a valuable Ring and when she saw it, the visitor from Karnaca next to her almost spilled her neighbor’s rum. Madam Natsiou raised her wine in toast. The lady from Baleton, full of beer, jumped onto the table, falling onto the guest in the center in the center seat, spilling the poor woman’s whiskey. Then Baroness Finch captivated them all with a story about her wild youth in Dunwall.

In the morning, there were four heirlooms under the table: the Snuff Tin, Bird Pendant, the War Medal, and the Ring.

But who owned each?

There are other ways of finding the lock combination without having to solve the riddle, but when I first came across it I was dead set on solving it. It did take me a couple of hours and a lot of scribbles, but I managed to figure it out. However, while I was frying my brain solving this riddle, I started to wonder: wouldn’t it be easier to write a program to solve this riddle for me? That’s what we will be doing in this blog post.

Initial setup Link to heading

Before we start writing code, we should begin by making our lives easier by clearly stating the entities of our riddle:

Name Heirloom Color Drink Origin
Winslow Snuff Tin White Absinthe Dabokva
Marcolla Bird Pendant Blue Rum Fraeport
Contee War Medal Green Wine Karnaca
Natsiou Ring Red Beer Baleton
Finch Diamond Purple Whiskey Dunwall

We also need to define how the solution will be structured. When I solved this riddle by hand I used a grid, and there’s no reason to not do the same here:

Far-left Left Middle Right Far-right
Origin
Drink
Color
Name
Heirloom

Initial setup (code) Link to heading

We will be using python as our programming language and OR-Tools as our constraint solver. Let’s start with a very basic MVP:

from ortools.sat.python import cp_model

RIDDLE_DATA = {
    "Name" : ['Winslow', 'Marcolla', 'Contee', 'Natsiou', 'Finch'],
    "Heirloom" : ['Snuff Tin', 'Bird Pendant', 'War Medal', 'Ring', 'Diamond'],
    "Color" : ['White', 'Blue', 'Green', 'Red', 'Purple'],
    "Drink" : ['Absinthe', 'Rum', 'Wine', 'Beer', 'Whiskey'],
    "Origin" : ['Dabokva', 'Fraeport', 'Karnaca', 'Baleton', 'Dunwall'],
}

FAR_LEFT, LEFT, MIDDLE, RIGHT, FAR_RIGHT = (0, 1, 2, 3, 4)

solution_grid = {}
model = cp_model.CpModel()

def setup_solution_grid():
    for category, entities in RIDDLE_DATA.items():
        solution_grid[category] = []

        for seat in range(5):
            solution_grid[category].append({})

            for entity in entities:
                solution_grid[category][seat][entity] = model.new_bool_var(f"{category}-{seat}-{entity}")

def solve() -> cp_model.CpSolver:
    solver = cp_model.CpSolver()
    status = solver.solve(model)

    assert status in (cp_model.OPTIMAL, cp_model.FEASIBLE)
    return solver

def debug_print(solver : cp_model.CpSolver):
    for category, entities in RIDDLE_DATA.items():
        print(f"{category}:")
        for seat in range(5):
            print(f"    Seat {seat}:")
            for entity in entities:
                value = solver.value(solution_grid[category][seat][entity])
                print(f"        {entity}: {value}")

if __name__ == "__main__":
    setup_solution_grid()
    solver = solve()
    debug_print(solver)

The most important thing to understand is the solution_grid variable. It has the following structure:

  • Category (Name, Heirloom, etc.)
    • Seat (0,1,2,3,4)
      • Entity (White, Blue, Green, etc. if the selected category was “Color”)

If, for example, you want to enforce that Countess Contee is at the far left (like it’s specified in the riddle), you can write the following code:

model.add(solution_grid["Name"][0]["Contee"] == 1)

Initial setup (basic constraints) Link to heading

If we run the code shown above, we get the following output:

PS C:\Users\Daniel\Desktop\github\blog\jindosh-riddle> python solver.py
Name:
    Seat 0:
        Winslow: 0
        Marcolla: 0
        Contee: 0
        Natsiou: 0
        Finch: 0
    Seat 1:
        Winslow: 0
        Marcolla: 0
        Contee: 0
        Natsiou: 0
        Finch: 0
    Seat 2:
        Winslow: 0
        Marcolla: 0
        Contee: 0
        Natsiou: 0
        Finch: 0
...

No value is selected for any grid cell, which obviously isn’t what we want. Let’s fix it:

def enforce_single_value_in_every_cell():
    for category, entities in RIDDLE_DATA.items():
        for seat in range(5):
            entity_total = 0

            for entity in entities:
                entity_total += solution_grid[category][seat][entity]
            
            model.Add(entity_total == 1)

This simple constraint solves our initial problem, but another crops up:

PS C:\Users\Daniel\Desktop\github\blog\jindosh-riddle> python solver.py
Name:
    Seat 0:
        Winslow: 1
        Marcolla: 0
        Contee: 0
        Natsiou: 0
        Finch: 0
    Seat 1:
        Winslow: 1
        Marcolla: 0
        Contee: 0
        Natsiou: 0
        Finch: 0
    Seat 2:
        Winslow: 1
        Marcolla: 0
        Contee: 0
        Natsiou: 0
        Finch: 0
...

Notice how Lady Winslow is selected for every seat at the table. This is obviously not the expected behaviour. This will require another constraint:

def enforce_different_values_for_every_category():
    for category, entities in RIDDLE_DATA.items():
        for entity in entities:
            seat_total = 0

            for seat in range(5):
                seat_total += solution_grid[category][seat][entity]
            
            model.Add(seat_total == 1)

Now every lady gets her own seat:

PS C:\Users\Daniel\Desktop\github\blog\jindosh-riddle> python solver.py
Name:
    Seat 0:
        Winslow: 0
        Marcolla: 0
        Contee: 0
        Natsiou: 1
        Finch: 0
    Seat 1:
        Winslow: 0
        Marcolla: 0
        Contee: 1
        Natsiou: 0
        Finch: 0
    Seat 2:
        Winslow: 1
        Marcolla: 0
        Contee: 0
        Natsiou: 0
        Finch: 0

The only thing missing now is a pretty-print functionality:

def print_grid(solver : cp_model.CpSolver):
    print()
    for category, entities in RIDDLE_DATA.items():
        if category == "Name":
            print("=" * (10 + 14 * 4 + 7))

        print(f"{category}:".ljust(10), end="")
        for seat in range(5):
            for entity in entities:
                value = solver.value(solution_grid[category][seat][entity])

                if value == 1:
                    print(entity.ljust(14), end="")
                    break
        print()
    print()

PS C:\Users\Daniel\Desktop\github\blog\jindosh-riddle> python solver.py

Origin:   Baleton       Karnaca       Dabokva       Fraeport      Dunwall
Drink:    Absinthe      Beer          Wine          Whiskey       Rum
Color:    Blue          Red           Green         White         Purple
=========================================================================
Name:     Contee        Marcolla      Natsiou       Winslow       Finch
Heirloom: Ring          Bird Pendant  Snuff Tin     War Medal     Diamond

Creating the constraints Link to heading

First paragraph Link to heading

The women sat in a row. They all wore different colors and Doctor Marcolla wore a jaunty white hat. Countess Contee was at the far left, next to the guest wearing a blue jacket. The lady in green sat left of someone in red. I remember that green outfit because the woman spilled her absinthe all over it. The traveller from Dabokva was dressed entirely in purple. When one of the dinner guests bragged about her Snuff Tin, the woman next to her said they were finer in Dabokva, where she lived.

Let’s enumerate the facts and strip away the riddle’s prose:

  • Marcolla wears white
  • Contee is at the far-left
  • The person next to Contee wears blue
  • Lady in green seats left of lady in red
  • Lady in green drinks Absinthe
  • Lady from Dabokva wears purple
  • Lady with Snuff Tin is next to lady from Dabokva

Now let’s enforce these facts in our program:

def enforce_first_paragraph():
    # Marcolla wears white
    # Lady in green drinks Absinthe
    # Lady from Dabokva wears purple
    for seat in range(5):
        model.Add(solution_grid["Name"][seat]["Marcolla"] == solution_grid["Color"][seat]["White"])
        model.Add(solution_grid['Color'][seat]["Green"] == solution_grid["Drink"][seat]["Absinthe"])
        model.Add(solution_grid["Origin"][seat]["Dabokva"] == solution_grid["Color"][seat]["Purple"])

    # Contee is at the far-left
    model.add(solution_grid["Name"][FAR_LEFT]["Contee"] == 1)

    # The person next to Contee wears blue
    enforce_a_next_to_b(("Name", "Contee"), ("Color", "Blue"))

    # Lady in green seats left of lady in red
    model.Add(solution_grid['Color'][FAR_LEFT]["Red"] == 0)
    for seat in range(5):
        left = seat - 1

        if left < 0:
            continue

        red_variable  = solution_grid['Color'][seat]["Red"]
        left_variable = solution_grid["Color"][left]["Green"]

        model.Add(left_variable == red_variable)

    # Lady with Snuff Tin is next to lady from Dabokva
    enforce_a_next_to_b(("Heirloom", "Snuff Tin"), ("Origin", "Dabokva"))

enforce_a_next_to_b is an auxiliary funcion that enforces “person with characteristic a is next to person with characteristic b”. This constraint shows up multiple times in both paragraphs, which justifies moving this logic to its own separate function:

def enforce_a_next_to_b(a : Tuple[str, str], b : Tuple[str, str]):
    a_category, a_entity = a
    b_category, b_entity = b

    for seat in range(5):
        left = seat - 1
        right = seat + 1

        middle_variable = solution_grid[a_category][seat][a_entity]

        if left >= 0:
            left_variable = solution_grid[b_category][left][b_entity]
        else:
            left_variable = 0
        
        if right < 5:
            right_variable = solution_grid[b_category][right][b_entity]
        else:
            right_variable = 0

        model.Add(middle_variable <= left_variable + right_variable)

A quick look at the solutions that the solver now provides shows that the constraints from the first paragraph are being enforced:

PS C:\Users\Daniel\Desktop\github\blog\jindosh-riddle> python solver.py

Origin:   Dabokva       Baleton       Karnaca       Fraeport      Dunwall
Drink:    Whiskey       Rum           Beer          Absinthe      Wine
Color:    Purple        Blue          White         Green         Red
=========================================================================
Name:     Contee        Winslow       Marcolla      Finch         Natsiou
Heirloom: War Medal     Snuff Tin     Bird Pendant  Ring          Diamond

165888 solutions

Second Paragraph Link to heading

So Lady Winslow showed off a prized Diamond, at which the lady from Fraeport scoffed, saying it was no match for her War Medal. Someone else carried a valuable Ring and when she saw it, the visitor from Karnaca next to her almost spilled her neighbor’s rum. Madam Natsiou raised her wine in toast. The lady from Baleton, full of beer, jumped onto the table, falling onto the guest in the center in the center seat, spilling the poor woman’s whiskey. Then Baroness Finch captivated them all with a story about her wild youth in Dunwall.

Lets once again enumerate the facts:

  • Winslow has the Diamond
  • Lady from Fraeport has the War Medal
  • Lady with Ring is next to lady from Karnaca
  • Lady from Karnaka is next to lady with Rum
  • Natsiou drinks Wine
  • Lady from Baleton drinks Beer
  • Lady in the center drinks Whiskey
  • Finch is from Dunwall

Enforcing these facts is pretty straightforward:

def enforce_second_paragraph():
    # Lady in the center drinks Whiskey
    model.Add(solution_grid["Drink"][MIDDLE]["Whiskey"] == 1)

    # Winslow has the Diamond
    # Lady from Fraeport has the War Medal
    # Natsiou drinks Wine
    # Lady from Baleton drinks Beer
    # Finch is from Dunwall
    for seat in range(5):
        model.Add(solution_grid["Name"][seat]["Winslow"] == solution_grid["Heirloom"][seat]["Diamond"])
        model.Add(solution_grid["Origin"][seat]["Fraeport"] == solution_grid["Heirloom"][seat]["War Medal"])
        model.Add(solution_grid["Name"][seat]["Natsiou"] == solution_grid["Drink"][seat]["Wine"])
        model.Add(solution_grid["Origin"][seat]["Baleton"] == solution_grid["Drink"][seat]["Beer"])
        model.Add(solution_grid["Name"][seat]["Finch"] == solution_grid["Origin"][seat]["Dunwall"])

    # Lady with Ring is next to lady from Karnaca
    # Lady from Karnaka is next to lady with Rum
    enforce_a_next_to_b(("Heirloom", "Ring"), ("Origin", "Karnaca"))
    enforce_a_next_to_b(("Origin", "Karnaca"), ("Drink", "Rum"))

And this is the final result:

Origin:   Dabokva       Karnaca       Fraeport      Dunwall       Baleton
Drink:    Rum           Wine          Whiskey       Absinthe      Beer
Color:    Purple        Blue          White         Green         Red
=========================================================================
Name:     Contee        Natsiou       Marcolla      Finch         Winslow
Heirloom: Ring          Snuff Tin     War Medal     Bird Pendant  Diamond

1 solution

Conclusion Link to heading

I was pleasantly surprised by how well the riddle’s facts mapped to python code. I had a lot of fun solving the riddle using constraint programming but it remains to be seen if simply solving the riddle by hand would be a quicker approach. It doesn’t really matter in the end: when it comes to games, the only metric that has ever mattered is whether or not you are having fun playing them.