Listener Crossword 4242: Killer Queen By Gwizardry

[jim360]

At times this was deeply frustrating -- after making a lot of progress all at once I lost track of what I knew and what I didn't. Eventually managed to make the breakthrough once I made use of a real pack of cards. So much easier to perform the shuffling with objects you can touch rather than in your head or on paper!

Mind you, this is the oddest Listener I've seen so far. I wonder what those who aren't exactly fans of numericals will make of this one. I enjoyed it, overall. And while the final step is optional, it makes the puzzle just much more complete to finish it. Thanks to gwizardry for a wonderful exercise in logic!

[sunny-dave]

Should be 'pack' - apologies for my transatlantic solecism - I blame Wink Martindale.

[AHearer]

This one has cured me of an obsession. For no deep (religious, for example) reasons card games leave me cold. I know that if we reduce it to its basics this is just another logic problem, as are most of the numericals, but I just can't be bothered.

When I think about it, I do crosswords such as the Listener because I enjoy the little rewards offered by each clue as well as the final pleasure that comes from the final stage(s). I admire the skill involved in setting and solving puzzles of this sort, but for me there's just not enough fun.

By the way, this week's Spectator was very clever. It would have made a worthy Listener if the testing of the solver's appreciation of the them had been a bit tougher.

[TheBear69]

I think the preamble is flawed. It says that "each player's hand is ordered by decreasing face value, except for pairs, as shown in the examples." And the examples include (AS 9S 2S); that would imply the order AKQJT98765432, as jim360 and others have stated. Hence the 'face value' of A must be a number bigger than 9. However, this is clearly contradicted by the first sentence of the last paragraph that indicates that the 'face values' of Q and A are 0 and 1 respectively. gwizardry should have used a different expression such as 'special face value' or 'adjusted face value' in that sentence. Or used the term 'rank' instead of 'face value' in the first two paragraph.

Regardless, I found this to be a much tougher than usual mathematical and enjoyed the challenge a lot. Thanks, gwizardry!

[TheBear69]

AHearer, you are of course entitled to your opinion, but I think that to dismiss this one because it has a card game as its theme is somewhat analogous to dismissing a thematic cryptic because it's an homage to some musician you do not care for. As you say, it's "just another logic problem" so there's no need for you to play poker, understand poker strategy or any other aspect of the game play. You've got 48 items to place in a 6x8 grid subject to a number of constraints...that's it.

My criteria for waht makes a good mathematical puzzle are:
a) is the search space large enough where brute force, trial and error methods won't?
b) is there a good entry point?
c) Is there a logical decutive path to the solution, or at least enough so that the search space is reduced to a small enough size where you can easily try various combinations?
d) Is there some aspect of the puzzle that gives it a unique twist which enhances the difficulty.

This puzzle succeeds on all those respects.

a) There are more than 25000 possible 3-card sequences that are 'legal' here so there more than 625,000,000 sextuplets to consider for each row. That's a big search space.

b) There is definitely a clear starting point for this one that you can infer from the clues.

c) Once you get started you can figure out a path. It's hard but fair.

d) The Q=0 variation really creates an interesting challenge.

I understand that for some the math puzzles are anathema, and that they are going to take one look at this and decide to pass. Fair enough. But for those that can appreciate a well-constructed math puzzle, this one is first rate.

[TheBear69]

I do think it's odd that the entry of the title is optional. I find it hard to imagine anyone getting it wrong if they have correctly filled the grid but I suppose it's possible. WIll an entry be marked wrong if the title is incorrect?

[jim360]

I'd have thought 48! ~ 10^61 was a simpler estimate of the parameter space (albeit an overestimate, given the ordering rules).

[tenflags]

Hello gwizardry ..
checked in now that I have the unique answer... as it happens I'm glad that the title is optional because as usual being Mr Thicky it isn't obvious to me and I'm very confident that every other aspect of the puzzle is correct (i.e. I have the unique grid)..
I shall try to resolve for completeness.. but am posting to say I enjoyed this clever piece of logic. Well done and thanks.
To be clear I am not seeking any response about the optional title.

[tenflags]

ahhhh got title now .. and I see TB69's point about it.

[jim360]

Said "solving path" may have been adapted a bit from how I actually did it in the first place. I was starting at my solution and trying to work out how I could justify certain steps, and found at times that I couldn't, but could justify things elsewhere.

Thanks for the comments gwizardry. I would be very interested to see how you set it all up!

[the_heisman]

Thanks gwizardry for a fascinating challenge
Good fun to have to get out a pack of cards. Clever to ensure a unique solution - at first I had thought some cards were interchangeable but they are not. To my embarrassment I cannot get the title although everything else is fine - or so I thought. The location of the last card particularly boggles my mind.

[Cruncher]

Still plodding through this with about half the grid filled but have managed to confirm the title, and therefore the location of those cards, so feel that things are going in the right direction. Hard on the brain!

[Cloverjo]

This is driving me nuts now. I have restarted it four or five times. I am pretty sure my initial steps are the way in. I am sure I have not made any unsubstantiated assumptions. But, each time, I come across something that means my working is wrong. I must be missing something or misunderstanding something. I started to use a real pack, but found it didn't help much when you don't know both the suit and the number of many of the cards.

[Scorpius]

Playing with a pack of cards shouldn't be at all necessary to solve the puzzle. These numerical Listeners should be solvable by logic alone, perhaps with some trial and error towards the end. Cloverjo's description of his frustration strikes a chord with me, as I have come up against an impasse repeatedly. However, I have started afresh and filled only those cells that can be deduced by logic and where I'm certain of my choices. I've now got 29 cells filled, including two entire rows and two entire columns.

Re the optional element, I don't see how the location of QH can possibly be determined, since the relevant columns/rows have no information about the distribution of suits. I assume therefore that it can only be determined in conjunction with whatever is revealed by the other specified cards. Perhaps that's why it's optional.

[jim360]

The location of QH is fixed by one piece of information in particular, so that there's no ambiguity about the final arrangement.

If you are having trouble cloverjo, I can recommend trying to fix the final suiting only after all the numbers are sorted. Not all the time, but it helps to treat the suits as a second piece of information that can often be left out until the final stage.

[emcee]

Late again due to gardening constraints!

After going down 2 (long) blind alleys I finally solved it last night. A brilliant, tough but perfectly fair logical problem. Calculator, pencil, a couple of tables to keep track of things were enough to see this through.

I too am amazed at the optional nature of the title. All I can see happening here is that it will let in those who tossed a coin to determine the final two entries in the grid - that doesn't seem right to me.

[the_heisman]

That's interesting emcee. I believe that I have no ambiguity notwithstanding my abject failure to understand the discretionary bit - which would I suppose make sense.

[Arcticpenguin]

I also agree with emcee. In my solution the ambiguity can only be resolved by solving the optional title. Am not a huge fan of numericals normally and had to do this stood up (because of low back pain) which was different. It was, however, very clever how it all worked through a little step at a time. Quite a feat. Well done Gwizardry. Can't wait for the next one !!!!

[olichant]

This was (for me) a slow solve, but a really enjoyable one. I am very fond of a few quiet hands of poker, not that it really helps in terms of the solving process for this puzzle. Jim has my total respect for knocking it off in a few hours. Really hope we get a setter's blog. I have no idea how one can set something like this up so that a relatively small amount of initial information can give rise to a coherent solving narrative and a unique solution.