Dominion Puzzle #1 Solution

The original puzzle:

In a solitaire game, find a way to have 8 Colonies in your deck by the end of your fifth turn.  (Outpost and Possession turns are included in this total.)  You may assume that you have perfect “shuffle luck”: i.e., you may rearrange your deck in any way you wish after shuffling.

Solution after the jump…The original solution, as provided by Jacob Davis, the author of the riddle, and also discovered by jonts26 and wmorgan:

Turn 1: Buy Ironworks

Turn 2: Buy Chancellor

Turn 3: Draw Ironworks, Chancellor, and 3 Copper.

1) Play Ironworks, gaining a Watchtower

2) Play Chancellor, discarding the deck, and buying a Throne Room.

Turn 4: Draw Throne Room, Ironworks, Chancellor, Watchtower, and Copper.

1) Play Throne Room – Ironworks, gaining two Bridges.

2) Play Watchtower, drawing 4 Coppers.

3) Play Chancellor, discarding the deck, and with the 5 Coppers, buy a King’s Court.

Turn 5: Draw Throne Room, King’s Court, Bridge, Ironworks, and Watchtower.

1) Play Throne Room – King’s Court – Bridge – Ironworks, gaining King’s Court/King’s Court/Bridge, each time revealing Watchtower and placing it on top of the draw pile.

2) Play Watchtower, drawing King’s Court, King’s Court, Bridge, Bridge, Chancellor, and Copper.  Play King’s Court – King’s Court – Bridge – Bridge – Chancellor.

3) At this point you have -$9 to all costs, $15, and 9 buys.  Play your Copper, and buy 8 Colonies at $2 each.

As it turns out, several readers came up with another solution (involving Nobles): decidedly less elegant, but rather more high-scoring.  guided was the first to send it in, along with James R, michaeljb, and papahav.  (The individual solutions are a little different, but basically the same idea of Ironworking Nobles.  For instance, the solution below is the one sent in by James; guided’s solution involved a Black Market.)

Turn 1: Buy Ironworks

Turn 2: Buy Chancellor

Turn 3: Draw 3 Coppers, Ironworks, Chancellor.  Play Ironworks, gain a Throne Room. Play Chancellor, discarding the deck, and 3 Copper, buy a Council Room.

Turn 4: Draw Ironworks, Throne Room, Chancellor, Council Room, Copper.  Play Throne Room – Ironworks, gaining a Watchtower and Bridge.  Play Council Room, drawing 4 Coppers.  Play Chancellor, discarding the deck, and 5 Coppers, buy a King’s Court.

Turn 5: Draw King’s Court, Throne Room, Ironworks, Watchtower, Bridge.  (Unless otherwise noted, gained cards are put on the draw pile using Watchtower.)

- Throne Room - King's Court - Bridge (x3)
            2x King's Court - Ironworks -> gain Nobles (draw Nobles)
                           x2 Ironworks -> gain King's Court
                           x3 Ironworks -> gain Ironworks

- Nobles (draw Council Room, King's Court, Ironworks)

- King's Court - Ironworks -> gain Ironworks
             2x Ironworks -> gain King's Court
             3x Ironworks -> gain King's Court

- Council Room (draw Ironworks, King's Court, King's Court, Chancellor)

- King's Court - King's Court - Ironworks -> gain Nobles (draw Nobles)
                            2x Ironworks -> gain Ironworks
                            3x Ironworks -> gain Ironworks
             2x King's Court - x3 Nobles (draw Ironworks, Ironworks, 7x Copper)
             3x King's Court - Ironworks -> gain King's Court
                            2x Ironworks -> gain King's Court
                            3x Ironworks -> Nobles (draw Nobles)

- Nobles (draw King's Court, King's Court, Estate)

- King's Court - King's Court - Ironworks -> gain Nobles (draw Nobles)
                            2x Ironworks -> gain Ironworks
                            3x Ironworks -> Nobles (discard, draw Ironworks)
             2x King's Court - Ironworks -> gain King's Court
                            2x Ironworks -> gain King's Court
                            3x Ironworks -> gain Ironworks
             3x King's Court - x3 Nobles (draw Ironworks, King's Court, King's Court, 2x Estate, Nobles)

- King's Court - King's Court - Ironworks -> gain Bridge (discard)
                            2x Ironworks -> gain Ironworks
                            3x Ironworks -> gain Nobles (discard, draw Ironworks)
             2x King's Court - Ironworks -> gain Bridge (discard)
                            2x Ironworks -> gain Ironworks
                            3x Ironworks -> gain Nobles (discard, draw Ironworks)
             3x King's Court - Ironworks -> gain Bridge (discard)
                            2x Ironworks -> gain King's Court
                            3x Ironworks -> gain King's Court

- Nobles (draw King's Court, King's Court, shuffle, Nobles)
- Nobles (draw Bridge, Bridge, Nobles)
- Nobles (draw Bridge)

- King's Court - King's Court - Bridge (x3)
             2x King's Court - Bridge (x3)
             3x King's Court - Bridge (x3)

Because Bridge was played 12 times, Colonies cost 0 and you have 12+ Buys.  Total cards used:

- 7 Coppers
- 3 Estates
- 1 Throne Room
- 1 Council Room
- 1 Watchtower
- 1 Chancellor
- 4 Bridges
- 7 Nobles
- 8 Ironworks
- 10 King's Courts

If you have any ideas for more such puzzles, please feel free to send them in!  We’d love to continue this series, but we are insufficiently clever to come up with puzzles as elegant as this one.

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35 Responses to Dominion Puzzle #1 Solution

  1. Manto says:

    Was my solution without Chancellor and 16 buys and colonies costing $0 valid? I submitted it to you guys last night.

    • theory says:

      I don’t see an email last night that doesn’t use Chancellor. Mind resending it?

      • Manto says:

        Cool, I just did send it in again through Contact Us tab. Here’s a link for it in case that didn’t get through:

        http://walkingideas.com/mantle/dominion/puzzle1.txt

        • DG says:

          In your solution Manto you use the ironworks to gain a great hall, use the watchtower to put it on top of your deck, and then draw a bridge from the top of your deck using the +1 card from the ironworks. I do not believe this is correct. If you trash this great hall I think you can still draw the bridge and complete the puzzle but you will need to amend your solution since you do play that great hall later.

          • Deadlock39 says:

            He can just not reveal watchtower at all when gaining it and send it to the discard too, but the solution would still need changed since it shows the Great Hall being drawn before the deck has been completely pulled into his hand.

          • Manto says:

            Thanks for checking over my solution DG,

            You are right – I was careless with the order in which I played Great Hall. Fortunately Great Hall can be picked up later when I empty the deck with a KC on CouncilRoom, keeping the solution intact.

            I’ve updated the link to correct the error that DG pointed out.

            • James says:

              I think (at least one) reason this might not work is on turn 2: you can’t play council room, “empty the deck” and still have cards in the discard pile. At that point you would reshuffle the cards into your deck and draw them.

              I think you have 2 estates and a Throne Room in your discard pile at that point. You only need one extra card from the CR, which means that there must be an estate left on top of your deck, which means it’s in your next hand.

              • Mick says:

                I could be off base or misreading the solution but if I’m not sorely mistaken as long as the deck is empty and no additional cards are needed the shuffle will wait until another card draw is called for. Since he has exactly the 4 cards remaining when the CR is played he should be fine. The rule is that a shuffle occurs only when there aren’t enough cards to complete a required draw or reveal, NOT just because the deck is emptied… (page 6 of the base set rules just before the blurb for Adventurer)

              • Manto says:

                James: End of Turn 3, there are 4 cards left on the deck. CouncilRoom draws 4, so that empties the deck. By rule, I cannot shuffle until I am actually drawing out the deck while the deck has no more cards.

                You said “at least one” reason why my solution may not work – feel free to post them here so I can respond to it.

                • James says:

                  I said “at least one” because there might be others, I don’t know.

                  I was just brain-farting on how many cards Council Room draws, never mind!

  2. michaeljb says:

    After I sent mine in, I later found some ways to make it a bit quicker, and I was going to format it nicer, but didn’t have time, what with being a college student during finals week.
    Anyway, I am very impressed with how elegant Jacob’s solution is, rather than requiring ~30 Actions played.
    Solving this puzzle made me wish solitaire mode on Isotropic had a “perfect shuffle luck” option, it’d make confirming a solution easier and the action chain of events could already be conveniently tracked.
    Looking forward to any future puzzles that get sent in…maybe I’ll have to get to work thinking up one myself.

  3. Cow says:

    The second solution is the one the I got (except I think Ironworks instead of Council Room makes my version a bit faster) and in hindsight it was very doable. It’s a fantastic puzzle with a lot of neat tricks, but it is logical as well.

    First, you need a card that allows you to play your best cards on turn 3, 4 and 5. That has to be chancellor. Then you need a card that gains other cards mid turn (before the buy phase) – that’s Ironworks. So there’s your opening.

    You also need a card that allows you to put cards back on the top of your deck – that’s watchtower. And you need a card that let’s you play other cards multiple times. That should be King’s Court, but you can’t get that turn 3, so turn 3 will have to be Ironworks -> Watchtower and buy Throne Room (or vica versa) while playing Chancellor to put everything back on top of the deck. Getting Watchtower here is key because you need it to draw coppers to buy King’s Court next turn.

    You also need a card that makes other cards cheap, particularly because that means you can draw them with Ironworks. And that card is bridge. So for turn four, Throne Room -> Ironworks -> (Bridge, Ironworks). The good news here is that you now have 2 actions and Watchtower lets you draw back up to 6 cards, Chancellor + 5 coppers, before playing the chancellor. And that means King’s Court.

    Now you just need to go infinite. Turn 5 is Throne’s Room -> King’s Court -> Bridge and then Ironworks. KC Bridge means 7′s now cost 4 so you can grab KC with Ironworks. However, there’s a bit of a problem here, namely you only start with 5 cards, and those were KC, Throne Room, Birdge, Ironworks, and Watchtower (which let’s you put everything you get on top of the deck). SO how do you draw the cards you just Ironworked? By the magic of getting Nobles with the first Ironworks. Nobles goes on your deck and you draw it immediately (Ironworks & Victory card) so it actually pops right into your hand. The next two Ironworks (from the KC->Ironworks) get two more KC’s. The top of your deck is now KC, KC and the Ironworks you got turn 4. Nobles lets you draw all 3.

    So:
    TR1 -> KC1 -> Br1,I1 (N1,KC2,KC3) and then N1 lets you draw (KC2,KC3,I2)

    So now your hand is KC,KC,Ironworks. And of course you play just that, and with the Ironworks you get Ironworks, Nobles, KC. The Nobles pops the Ironworks into your hand, and that is your 2nd stacked KC play. Now get Ironworks, Ironworks, Nobles. Now the Nobles pops the Nobles into your hand. Your third stacked KC play is Nobles, which draws 9 cards and leave you with KC,Ironworks,Ironworks and Nobles (and chancellor and 5 coppers and watchtower) in Hand.

    (So that looked like:
    KC2 -> KC3 -> I2 (I3,N2,KC4), I3(I4,I5,N3), N2 (drawing everything)
    and your hand is KC4,I4,I5,N3 + others

    At this point you can stop buying nobles and buy Council Room to get you more buys in the end.
    Now:
    KC2 -> KC4 -> I4(I6,I7,B2),I5(CR1,KC5,KC6),N3(drawing everything)

    Now your hand is KC5,KC6,I6,I7,B2,CR1 + others. We’re on our last KC2 so we need KC5 to restart that, so the hand is really KC6,I6,I7,B2,CR1 with three new KC5 cards waiting to be played. Start with KC6 and then play I6 and I7 to get 2 more bridges
    KC2(last) -> KC5
    KC5->KC6->I6(B3,KC7,KC8),I7(KC9,CR2,I8),CR1(draw everything)
    KC5->KC7->B2,I8(KC10,I9,CR3),CR2(draw everything)
    KC5->KC8->

    KC8->KC9->I9(B4,B5,B6),I10(B7,B8,B9),CR3(draw everything)
    KC8->KC10->B3,B4,B5
    KC8->B6
    B7,B8,B9

    Which gives you a total of 21 bridges and 9 council rooms, pricing everything at zero and allowing you to clean out all the colonies, provinces, duchies and nobles (we needed to buy 5 more) leaving you two more buys – get something nice for mom and dad!

    • Fuu says:

      “It’s a fantastic puzzle with a lot of neat tricks, but it is logical as well.”

      Yes I was thinking the same. The puzzle has those specific requirements (gaining cards mid-turn, etc) which only a few cards can satisfy. Because of this I wonder whether it is possible to come up with subsequent puzzles which don’t require these key cards.

    • michaeljb says:

      My solution actually doesn’t use Watchtower. I fiddled with it a little but gave up on it much sooner than I should have. Obviously, this meant the most challenging thing for me was figuring out how to draw through all the Coppers and Estates, and that took a lot of time to put together, but it was satisfying to see completed. And I had fun doing it, so I’m not too bummed out I ended up picking probably the hardest way to do it lol

  4. Jahz says:

    Nice and sweet!
    So the question for me now is the following: do we actually learn something for classic play or not ?
    In one way I would say no, because everything here is totally scripted, but in the other hand, well, the tricks with KC / Ironworks / watchtowers / bridges are definitely interesting, and may be used in real game even if in a less perfect way than here.
    But most of the time a bit less than perfect is enough to win (like if you were almost to play the famous KC/KC/Bridge/Bridge/Bridge, you should win anyway).

  5. timchen says:

    It is somewhat interesting that I knew about this ironworks+noble+bridge+KC trick by heart yet I missed the solution. It seems that the key card, Watchtower somehow resists to be in my mind.

    The hardness of the problem, for me, is that you cannot really do anything big before turn 5. I was pretty sure that you cannot get two KCs before turn 5 (unless you give up pretty much anything else), and that makes me start to think something on an entirely different line– which of course does not work.

    In the original solution, the Watchtower sort of steal a turn in turn 5. The closest experience I have is in some crazy game I can actually buy 2KCs and 3 Bridges and I have a Watchtower in hand. I guess it just eludes me that you can gain cards, put them on deck and then draw them.

  6. DG says:

    The solution that I found was very similar to the original solution but gaining an ironworks and conspirator on turn 4, drawing them with the watchtower, gaining a bridge and buying the king’s court. Turn 5 then can use the second ironworks for more cards, the conspirator for more draws, but is essentially the same as the original solution.

    The are probably many other small variations too.

  7. Arya Stark says:

    haha, who says chancellor is the worst card of all! it is good for something

    • Kazz says:

      well, yes, if you can precisely determine what you’re going to draw the following turn, chancellor is great.

  8. Kazz says:

    I guessed all the cards in the solution, I just never bothered to play out the actual solution. Glad to see I had decent instincts.

  9. Fuu says:

    An elegant solution. I was expecting something more along the lines of the long-action brute-force solution, but that first one is impressive.

    Turn three seems to be the pivotal moment. Ironworks and Chancellor to gain Watchtower and Throne Room on the flipped deck, all four of which are drawn in turn four. I certainly didn’t come up with that, and spent some time instead working around Throne Room and Chancellor to gain King’s Court. That was never going to work.

  10. lefaiison says:

    Nice solutions! I had the general idea of how to solve the puzzle but not actually get some of the pivotal moves.

    I think a natural extension of this problem is if it’s possible to get a score of -10 AND end the game in turn 5. I think it’s possible although I haven’t solved it yet. It has the additional challenge that you need to get rid of the starting 3 estates as well you can’t use nobles to continue your chain since they’re worth points.

    • chesskidnate says:

      did you mean get a score of 0?

      • Personman says:

        I’m pretty sure he means -10, i.e., get all the curses and get rid of all your estates and gain no other VP and end the game (presumably on piles, since ending it on Provinces might interfere with the whole negative score thing ;)

    • Cow says:

      My guess is that this is impossible because you need to play nobles early in turn 5 and you can’t get them back to trash. However, I am almost certain that you can gain and trash 8 provinces, buy 10 curses and end up with negative 4.

  11. linger says:

    Am I missing something, or isn’t it impossible to gain Nobles with Ironworks?

  12. chachi says:

    is isotropic down? i can’t log on to save my life, so I got on BSW instead. God, that was a mistake. That site is horrible. I’d rather play monopoly to the end than Dominion on BSW.

  13. jimjam says:

    Would you guys be interested in this kind of puzzle (i.e. would never occur realistically):
    Starting with 8 ironworks in hand and nothing in deck, how many VP can you get in one turn?
    Can you get a colony and a province in one turn, this time with 9 ironworks in hand?

  14. Ragnar says:

    Has anyone worked out the probability of this working given the card setup? I’ve tried it on isotropic about 30 times and haven’t come even close. For one, you need to start off with a 3/4 split, which is a probability of 11/12. Obviously things get a lot steeper from there.

  15. guided says:

    Finally getting around to commenting on this…

    The first solution is kind of stunning in its simplicity. Bravo. Mine involved a vastly more complicated final turn than even the 2nd solution above ;)

    I rather enjoy my solution though since it involves some cute little tricks not present above:

    1. Black Market + 2xQuarry to reduce the cost of action cards to where I can gain anything with Ironworks.
    2. Since the solution also required more than 10 Kingdom cards, I relied on Black Market to get me a single copy of a couple other cards I needed beyond the 10 available Kingdom piles.
    3. KC/Upgrade to convert my three initial Estates into $7 action cards :D
    4. Similarly, KC/Expand to convert three Coppers to action cards worth up to $7.

    • vidicate says:

      You still ended up needing Watchtower, yes? No? Have you posted the solution on the BGG? I’d love to see it.

      • guided says:

        I’ll just post it here, though the formatting may get horribly broken:

        Kingdom:
        
        Black Market (BM)
        Bridge (Br)
        Chancellor (Ch)
        Ironworks (IW)
        Quarry (Qu)
        Throne Room (TR)
        Watchtower (Wat)
        Nobles (Nob)
        Expand (Exp)
        King's Court (KC)
        
        The first 2 Black Market pulls will include Upgrade (Upg) and Library (Lib).
        
        
        Opening: IW1/Ch
        
        Turn 3: IW1 (Wat1), Ch. $5. Buy TR1.
        
        Turn 4 Hand: TR1/IW1/Wat1/Ch/Cop.
        Play TR1/IW1, gain TR2/IW2 on top of deck. 2 actions left.
        Play Wat1. Current hand: TR2/IW2/Ch/3xCop
        Play TR2/IW2, gain Qu1/BM.
        Play Ch, discarding the deck.
        Buy Qu2.
        
        
        
        Turn 5 Hand: TR1/TR2/IW1/IW2/Wat1
        Draw pile: Qu1/Qu2/BM/Ch/3xEst/7xCop
        
        
        Play TR1/TR2/IW1/IW2 to gain 4 cards, top-decking the first 3 with Wat1.
        1. Wat2
        2. TR3
        3. IW3
        4. Wat3 (discarding it)
        
        *4 actions remaining.
        
        Play Wat1, drawing 6 cards: Wat2/TR3/IW3/Qu1/Qu2/BM.
        Play TR3/BM.
        Play Qu1/Qu2.
        Buy Upg for $1, top-decking with Wat2.
        Buy Lib for $1, top-decking.
        Play IW3, gaining KC1 ($3 value), top-decking.
        Play Wat2, drawing 6 cards: KC1/Upg/Lib/Ch/2xEst
        
        *1 action remaining. $4. Action cards reduced $4.
        
        Play KC1/Upg:
        1. Draw Est. Trash Est. Gain KC2.
        2. Draw Cop. Trash Est. Gain KC3.
        3. Draw Cop. Trash Est. Gain Exp.
        
        Play Ch, discarding the deck. +$2.
        Play Lib, drawing 5 Cards: KC2/KC3/Exp/Wat3/Cop
        
        *1 action remaining. $6.
        Hand: KC2/KC3/Exp/Wat3/3xCop
        Draw pile: 4xCop
        
        Play KC2/KC3, allowing 3 action cards to be played 3x:
        1. Exp
        a. Cop->KC4, top-decking with Wat3.
        b. Cop->IW4, top-decking.
        c. Cop->IW5, top-decking.
        2. Wat3, drawing 6 cards: KC4/IW4/IW5/3xCop
        3. KC4:
        
        Three more action cards 3x:
        1. IW4, gaining IW6/KC5/KC6
        2. IW5
        a. IW7
        b. Nob1, drawing Cop.
        c. Nob2, reshuffling and drawing Nob1.
        3. Nob1, drawing all cards.
        
        *6 actions remaining. $6.
        Hand: KC5/KC6/IW6/IW7/Nob2/4xCop
        
        Play KC5/KC6:
        1. IW6, gaining KC7/KC8/Br1
        2. IW7, gaining Br2/Br3/Br4
        3. Nob2, drawing all cards.
        
        *11 actions remaining. $6.
        Hand: KC7/KC8/Br1/Br2/Br3/Br4/4xCop
        
        Play KC7/KC8/Br1/Br3/Br3.
        Play Br4.
        Play 4xCop.
        Have $20 and 11 buys. All prices reduced by $10.
        Buy 8 Colonies for $8 and 3 Provinces for free.
        

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