Game on (6 June 2021)

Last week I asked the following questions:

  • Which suits have all 13 cards appearing at least once?
  • Assuming you answered “more than zero”, can we actually remove a suit (regardless of identity of face-down cards)?

Bart Wright had some vague intuition that it might be possible. Judging from his writing, I think he would have some valuable management skills to contribute to any company who is interested in hiring. Unfortunately, he failed the “specific/measurable/achievable/relevant/time-bound” test. Schistocerca Americana has found a solution: Diamonds is the only suit with each card appearing at least once. His solution is as follows:

Deal – Do Nothing

1st Draw – ed

2nd Draw – hj, hf, dh, da, eb

3rd Draw – fb, hf, cg, eg, ig

4th Draw – ja, ji, ji, jd, fj, eg, fg, ei, gi, ga, ch

5th Draw – da, ad, ab, ib, ab, jb, af, aj, aj, ij, fj, hd, hj

The result is shown below. Using cut-n-paste in Excel proves this solution is indeed valid with no illegal moves, sloppy explanations or typos.

To be honest, I didn’t try to solve this problem myself since I am currently working on another fun project that is unrelated to Spider Solitaire. Well done to Bart Wright and Schistocerca Americana for their excellent contribution to this blog.

Of course, we are interested in removing eight suits instead of one. Clearly it makes sense to look for easy turnovers and empty columns at the beginning of the game. But the above was not an exercise in futility. At least we know that it’s possible to remove a suit just by sheer power of information (i.e. knowing the identity of unseen cards) even without an empty column. Besides an aspiring player must (i) learn to analyse long move-sequences involving a large number of face-up cards when playing without undo (ii) learn to play the cards well even when there is no empty column 😊

Let us first focus on exposing as many turnovers as possible without dealing any cards from the stock. Experimentation shows it is easy enough to turn over many cards in the tableau, including all cards in column 2:

Further experimentation with undo leads to the following cheat sheet:

It’s time for another fun question: how many rows do we need to deal from the stock to be sure of procuring an empty column (assuming the worst possible permutation of unseen cards)?

Note that NaN may be a valid answer if this turns out to be impossible even allowing for dealing all cards from the stock.

6 thoughts on “Game on (6 June 2021)

  1. I plead guilty to vagueness on the last problem, though (to act like a whiny child) you didn’t say there would be a “specific/measurable/achievable/relevant/time-bound” test. Nyah-nyah.

    Of course specific is better. But… you and “Schistocerca Americana” (is there a nickname there?) seem to have tools to work with that I don’t have. Is “AncientExcel CheeterSheeter” a real thing, perhaps referred to here by a whimsical name? “SA” spoke of using lots of undo. Do you have a tool that allows Undo automatically? Moving cards around in an ordinary (?) spreadsheet page with cut and paste, in which individual steps can be undone? It’s hard for me to imagine being specific about a solution without a great deal of laborious work given the tools I know of and know how to use (keeping track of previous steps by hand, to reliably know how to undo?).

    Given the tools I now have, I’m not even going to try this week’s problem. It might be beyond what I could solve even if I did have tools, but the lack of tools is the first stumbling block.

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    1. Esteemed Scholar Bart, Schistocerca Americana is a reference to the main character from the 1972 Pilot for the TV series “Kung Fu” starring David Carradine as Caine, a Shaolin Priest. At one point in his training a blind monk asks Caine if he can hear the grasshopper walking on the sand at his feet. Caine of course says, “No, how can you hear these things, Master?”; to which the blind monk replies; “How can you not hear them?”. From then on the monk gave Caine, his favorite student, the nickname Grasshopper. As I have deemed our host as “Master T” and assume my roll as Student, I become American Grasshopper or Schistocerca Americana. I have tried to honor Master T’s ability to see much much further into complicated moves that I could ever hope to and also to play on his using animals in his stories.

      “AncientExcel CheeterSheeter” is indeed something I created. I have not passed it along to anyone.

      Ancient Excel refers to the fact that I am still using Excel 2003.

      The whole world says “Cheat Sheet”. I am silly so I say CheeterSheeter.

      It uses cells made up to show 104 cards, suit and rank, that I can drag and drop into a ten column active area. I can use ctrl+Z to undo moves but Excel is limited to 16 undos. I had to make a registry edit to increase that to 75. Don’t like going in there!

      I made it because I often have trouble distinguishing clubs from spades in Microsoft Solitaire Collection. Until this Game I have not used it as a trial and error aid to solve problems before posting my initial comments. I just “set the table” to the current game status and then stare and move things in my head. After I post my comments I then do the drop and drag routine to see if I errored in my mental gymnastics. I also have used it to “play out” both your and Master T’s solutions.

      So yes, this gave me an unfair ability to find an exact solution to the Diamond run. Without it I could not have gotten any further than you did, perhaps not as far. It is just too much information for me.

      I tried to post a screenshot of my AncientExcel CheeterSheeter to this blog but with no success. I will send Master T an email with a screenshot and he can post it if he sees fit.

      At the risk of being too verbose, I actually found the solution while trying to prove that a Diamond run could NOT be done, by going to the end and proving that some necessary cards would be trapped. So I would work backwards to find a trapped card then return to start and work forward to try to avoid the trap. Backward, forward, backwards and forwards……. Did this for four hours.

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      1. Thanks so much for explaining.

        So are you also old enough to have been around when Kung Fu was on in the original season? I watched many episodes and liked that show. Grasshopper. So you’re grasshopper. Fair enough. The Wikipedia article on that bug was interesting (but I love going down that sort of little path).

        And thanks for explaining the CheatSheet thing. “Registry Edit”. Yup, kind of makes a person nervous. I had to do it fairly often as part of my last job. Which was an English to Japanese machine translation system. We started on it in 1990 and it may contain one of the best rule-based English parsers around, but since then the “big data” method has surpassed rule-based systems and the technology is obsolete and kind of was when I retired in 2012.

        Trouble telling clubs from spades. I don’t see the basis for that right away. I’ve had trouble distinguishing suits in some of the diagrams in this blog, but not there.

        Four hours to work on one of these puzzles… I guess I might if I was in the right mood. I’ve enjoyed some of the puzzles at “538 riddler” (but fewer lately) and did lots of “Advent of Code” puzzles (relevant to programmers, retired or active), and some of those might have taken me 4 hours or more.

        And, seeing your comment on my solution just come in, it’s nice to know you didn’t spot any glaring errors. I realized after posting that there are a variety of ways of going about it, like using the 7s in the opposite order.

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  2. Master T, this appears to be as easy as the last assignment was hard. This always makes me nervous that I am the only one in the room overlooking something obvious.

    How many rows do we need to deal from the stock to be sure of procuring an empty column?

    Well, we can only look to create a void in Col 2. We need to move the 8 but have no 9.

    Draws 1 ‘n 2 cover our 8 with two 6’s and give no 7’s. Things is not lookin’ good.

    But 3rd draw quickly clears it all up. We cover with a J but get a Q, then the two 6’s go to the two 7’s and we look around for a 9 and it is under the 10, said 10 cleverly unblocking by joining the J.

    8 on the 9 and presto – void

    Answer: 3 rows

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    1. SA, your proposed solution and the idea that it might be an easy problem gave me courage to look at it. I think your solution shows that we can do it with 3 deals. I agree with your steps.

      One of the things that made my eyes glaze over was looking at the cheat sheet and assuming all those cards in column 2 were still in their starting locations. But I guess they aren’t — we’ve moved them as the deal diagram shows before we begin on this problem.

      I think I can do it with 2 deals (and I’ll try to be precise, grumpy Master). We start with lots of those cards from the diagram uncovered, but there are a few cards that are in fact covered where we know their identity. While the GM says “it is easy to turn over many cards in the tableau”, that does not mean that he has in fact turned over all the ones that would be helpful that we would ordinarily do, a clever sort of misdirection to solvers.

      Of great interest is the 7 that is lurking under the 10 in column 1. We have a jack to accept the 10, and then we have two 7s exposed. If we can dig out one of those 7s after the first deal we can drop an offending 6 on it, and if we can clear another after the 2nd deal, we drop the 6 from the 2nd deal onto it Then we can move the 8 to win.

      First, to get organized, we want to have a receiving queen in column 4 instead of 10, so we move that jack before we do the first deal. Then we move the ten, uncovering the 7.

      After the first deal, db exposes the queen, ad uncovers our first 7, and ba gets rid of our first 6 (good thing that 5 and 6 are in-suit). To keep the other 7 near the surface, we move that 3 over, ge.

      After the second deal, gc re-exposes that 7, bg removes the 2nd offending 6, and bf wins!

      Before deal: dj,aj
      After deal 1: db,ad,ba,ge
      After deal 2: gc,bg,bf

      We can’t possibly do it with 0 or 1 deals, because there is simply no 9 anywhere to receive that 8 until after the 2nd deal.

      The odds are there’s some mistake in there, maybe a stupid mistake, maybe a profound one, but that’s my bid.

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