Game on (4th July 2021)

Continuing on

from last week: this is the current state of play with the Good Guys able to obtain three empty columns

Bart has correctly identified 11 guaranteed turnovers. He also identified the number of turnovers in each individual column and added up correctly. Unfortunately, he blew it all in the last step by submitting a final answer of 13 instead of 11. Bwahhahahahahahahahahah 😊

SA did some analysis, but didn’t give a bottom-line-up-front saying “the answer is XYZ”. Bwahhahahahahahahahahah to him as well 😊

Going back to the game, let us take our three empty columns and guaranteed turnovers.

Not surprisingly we get more than our minimum turnovers. Some simple experimentation gives us three bonus turnovers (highlighted) in columns 8 and 10. I did not make a serious effort to uncover the last two cards. Now is the time to focus on tidying up.

By this stage we should be close to claiming a lock. With only two unknown cards the game pretty much plays like Freecell – and it is well known that Freecell is almost always won with perfect play. Here, we note that all cards in Hearts are visible after the third round is dealt.

Note that once we determine either card, the other follows by the process of elimination 😊 The last two unknown cards should be the 4 of Diamonds and 9 of Spades in some order.

QUESTION: Starting from the previous position with score = 109(*) give a sequence of moves leading to the removal of the Heart suit after the third round (do not continue after removing Hearts). Alternatively, if you believe this to be impossible then give a sequence of moves leading to the “best possible clean up” before dealing the second round.

(*) Obviously it will be much less than 109 since I had to make some moves to work out the identity of face-down cards, but it’s not worth the effort of doing another screen-dump just to change the number 109 to something else.

5 thoughts on “Game on (4th July 2021)

  1. To the previous week’s puzzle, I gave a final answer of 13, but GM says it should have been 11.

    In trying to resolve the discrepancy, I think perhaps we were defining the problem differently. When GM said we could use “undo”, perhaps he was saying that we could go forward from the initial position and then undo back to that initial position, but not backwards beyond that point. I indeed broke my own analysis down into what could be done with that assumption, whence I got 11, but then looked at what I could accomplish if I did go back beyond that point, including undoing the deal, and believe I found two more cards that could be uncovered, in columns 8 and 9. I think my write-up contains sufficiently explicit directions that people can evaluate whether or not I succeeded given my assumptions. The column 9 turnover seems particularly easy to verify.

    SA gave me a smile and a bow (thank you!) and did not cry foul with regard to my expanded undo assumptions — though of course one can give a smile and bow without verifying every detail.

    If we are allowing “undo”, we should give it free rein and not put artificial limits on its use!

    As for this week’s problem, I can sketch out how it can be done. It has quite a few “degrees of freedom” and varied possibilities and spare spaces. No single, long, clever sequence is required. But a sketch is exactly what GM did not want to see. He asked for specific steps, and that is too much for me to keep track of in my head. So I’ll leave it someone else to do that, perhaps SA armed with his cheeter-sheeter.

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    1. Esteemed Scholar B, I did indeed use my AncientExcel CheeterSheeter to add a third visual aid as described in my post for this week. After going through the exercise I came up with a solution that, if correct, made the use of the third visual aid unnecessary, but it was necessary to use it to prove it’s unnecessariness.

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  2. Here is how I would approach this.

    Our objective: Give a sequence of moves leading to the removal of the Heart suit after the third round.

    If the idea is to use just the Screen Shot of Position 109 and the Cheat Sheet provided by Master Chi-Yuen I plead incapability. NoCanDo. I need one more CheeterSheeter that shows the cards above the visible cards in Position 109. So I am using three aids, call them TO’s (Turn Overs), Visible (Position 109), and Draws (the first three rows of Master Chi-Yuen’s Cheat Sheet).

    Let’s count cards. Of the 26 Hearts we have three that of which only one card is available to us, K, 9 and 7. Furthermore we have a run available without using any of the TO’s. At a glance all the Hearts in the TO’s section are hopelessly buried.

    So let’s proceed on just using Hearts in Visible and Draws. If this works it means that we could have worked this out with no more visual aids than those two provided by Master Chi-Yuen as we won’t turn over any new cards.

    From Position 109 clear access to the Heart 10 in Col 5

    dh, dc, ec ……grouping the diamonds helps my visualization.

    Make Col 7 Atomic and the move the Spade Ace from Col 6 to 8

    ga, gh, ah, fh

    Col 2 will become a disaster zone with 6’s being drawn twice so move the 6 & 4 of Hearts to Col 6 using void in Col 7

    gi, bg, ag, ba, bf, af, ga, gf, ig

    Take the first draw

    Stack some Diamonds in Col 2. Clear access to the Heart 4 in Col 6 and cover with the 3.

    Db, eb, fc, gf,

    Take second draw

    Clear the Heart 10 and cover with the 9, 8

    eb, fe, ie

    Replace the Spade 5 in Col 6 with Heart 5 currently residing in Col 2 using void in Col 7

    gc, gi, fb, fg, bf

    Getting really iffy here.

    Take last draw

    Clear Heart Ace in Col 3 and join with duce

    ch, ca

    Clear the Heart 8 in Col 5

    eh

    Clear Heart 6 thru 3 in Col 6

    fb

    Do the Heart run

    ge, fe, ae

    Surely there is something wrong somewhere but this is my XYZ

    Take 10 aspirin, lie down, close eyes, place cool damp towel on forehead.

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    1. Impressive that you could go through it all. However, I think you start with a wrong assumption. You speak of doing the first deal, the second deal, and then the third deal. However, the first deal has already been done before we start working on this problem. You can verify this by for instance counting the aces of spades and finding three of them, one on the board and two in the deals. Given how few hearts there are in that first deal, you probably solved a harder problem than the one that GM posed for us.

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      1. Esteemed Scholar Bart, yes, thank you, I did indeed start from the wrong place. How can I do that?? I get so narrow focused on problem solving that I totally miss that I am not trying to solve what is requested.

        I was playing with a deck of 114 cards. I think this made the task easier rather than harder because, at a first glance, it becomes critical to protect the availability of the Heart 3 in Col 7 as the other Heart 3 in Col 8 is buried. I, of course, had an extra Heart 3 to play with.

        I think a Heart run is do-able and perhaps I will take a closer look and another stab at it later this week.

        I should grade myself this week as achieving both highest and lowest honors, a solid 10 for effort and a solid zero, nada, zilch, goose egg, for accomplishment.

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