8
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It was yet another dreary Friday afternoon. Hardly anybody to talk to and the internet connection was flaky as usual. And the less said about his latest performance review the better. Hardly anything to look at either, except for this dreaded “demotivational poster” hanging on the wall. Apparently, the boss only got ‘C’ in Year 10 art. enter image description here

Yesterday Joe Bloggs had a clever thought. Suppose he could remove the apostrophe and the happystar. Then he could treat the black letters as part of a 4x4 sliding block puzzle. With a bit of luck he could rearrange these letters to spell a much more positive message. But try as he might, when Joe experimented with a set of Scrabble tiles the best he could achieve was DEAD PIGS FLY TONW. At least the poster didn’t mention anything about procrastination.

Joe stared at his computer screen. Not the most promising game state, but he had seen worse. At least he had one empty column and had turned over most of the cards in the tableau. It would be tempting to reveal another face-down card in column 8 but at this point in the game Joe desperately needed to complete a full suit.

enter image description here

Perhaps Joe could increase his chances ever so slightly if he could swap the J-0-9-8-7-6-5-4-3 in column 1 with the J-0-9 in column 2. Then he would have a run of three cards, K-Q-J in Spades. Together with the length-7 straight flush in Spades in Column 6, he might get lucky enough to complete Spades after dealing the final round from the stock. Not much, but better than nothing. After scanning for other possibilities he found nothing better. The goal was decided: Obtain K-Q-J of Spades in column 1, then turnover a card in column 8.

Questions:

(1) How Can Joe Bloggs achieve his goal?

(2) What is the significance of the sliding block puzzle in the above story?

Note: it is assumed the reader knows the rules of Spider Solitaire since this information is easily found online.

Text format of current game state (? = face-down card):

????? 9h 8h 7c 6c 5c 4c 3s 2s As Jd Qc Jd Ks Qs Jc 0c 9c 8c 7h 6h 5h 4h 3h

? 9d 8c 7s 6s 5h Js 4s Kd Qs Js 0h 9h

8d 7d 6d 5d 4d 3d 2d Ad Ac

4h 7c

Ah

Kh Qh Jh 0d 9d 8d 7d Kc Qc Jc 0c 9s 8s 7s 6s 5s 4s 3s

Kd

?? 4d 3d 2d Ad 6d

2c Ac Kh Qh Jh 0h 9s 8s 7h 6h 5d 4c 3c 2c Ah

empty-column

Stock = 10

Checksum: 28+13+9+2+1+18+1+7+15+0+(1x10) = 104

Text format of sliding block puzzle:

Row 1 = D, E, A, D

Row 2 = P, I, G, S

Row 3 = W, O, N, T

Row 4 = F, L, Y, blank

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6
  • $\begingroup$ The two D's in the sliding block puzzle mean that all arrangements of the letters are accessible. I am guessing that one of the top corner squares finishes with a D but it must be the other one. I don't know how that helps the spider. $\endgroup$ Commented May 30, 2023 at 13:29
  • $\begingroup$ Ross Millikan, yes that is correct. Now onto the spider! $\endgroup$
    – happystar
    Commented Jun 1, 2023 at 9:41
  • $\begingroup$ Do you know if there's a way to get the spider solitaire state into a better screenshot? or better yet, an interactive version :) $\endgroup$
    – JGibbers
    Commented Feb 22 at 16:42
  • $\begingroup$ Unfortunately I don't have an interactive version. I have an AI that plays Spider without undoing any moves (available at GitHub) but it wasn't really designed for this type of question. $\endgroup$
    – happystar
    Commented Apr 7 at 22:08
  • $\begingroup$ When I knew the title, I instantly knew that it is your puzzle :) $\endgroup$ Commented Apr 8 at 1:37

1 Answer 1

2
+500
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Spider

Since there are no open Queens nor Jacks and the Jack of spades is followed by a 10 of different suit, it is actually impossible to just swap the Jacks and below for the two columns. However, what Joe can do to achieve the goal is to swap the two Queens of spades as well.

I don't have any handy way of creating playing card graphics, so I will just notate the moves as
cX->cY
which means that we move from column X to column Y by using the empty column as an intermediate step if necessary. So, e.g., the first step, c1->c2 would consist of first moving the 7h-3h to the empty column, then 8c to the second column and then the 7h-3h from empty column to the second column. Now, Joe can achieve the goal by following these steps:
1. c1->c2
2. c1->c7
3. c2->c7 (At this point first column Q and below moved to column seven)
4. c2->c1 (Column 2 Q and below moved to column 1)
5. c7->c1
6. c7->c2
7. c1->c2 (First columns Q and below moved from column 7 to column 2)

Then, to turnover the card in column 8, it is enough to do

8. c8->c4
9. c8->c10

Sliding block

If Joe wants to rearrange the letters to

D E A D
P I G S
F L Y T
O N W


by only moving the last two rows, then this is impossible due to parity arguments. However, since there are two Ds in the puzzle, all the odd permutations are possible by swapping the two Ds as well. Thus, much like in the Spider puzzle it was impossible to achieve the goal without swapping the two identical queens, here it is impossible to achieve the goal without swapping the two identical Ds.

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2
  • $\begingroup$ This answer is correct, except Joe wants to rearrange the letters to DEAD PIGS FLY TOWN :) $\endgroup$
    – happystar
    Commented Apr 7 at 22:11
  • 1
    $\begingroup$ @happystar I guess that makes more sense but that's not what the question says :) $\endgroup$
    – user39583
    Commented Apr 8 at 6:56

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