This is the fifth Chain Puzzle in the Tabletop Games series, in which all puzzles are themed around board games, card games, tile games, and the like. The answer to this puzzle is a thematic word or phrase. The solver whose answer is awarded the green checkmark has first refusal on the opportunity to create the next puzzle in the series, which must somehow incorporate the answer to this puzzle somewhere within its construction. The solver is under no obligation to create the next puzzle - in the event that the solver does not wish to take up this opportunity, the puzzle's setter may take up the offer of a willing substitute setter or choose to continue the chain themselves.

The answer to the previous puzzle (which provided the theme for this one) was YAHTZEE.

We were low on numbers at this week's neighbourhood games night - only four of us could make it. My friend - our host - was very apologetic as she ushered me in to the games room, where I spied upon the table a Yahtzee scorecard, a scrap of paper, and several black, white and red dice.

"Ah, we're playing Yahtzee then!" I exclaimed.

"No, sorry," said my friend. "You're still not used to this set-up yet, are you?! I have carefully arranged some components from my Yahtzee set in such a way that you can use them to solve two different grid deduction puzzles. Do that, and you should be able to work out what game we're actually playing tonight."

Here's what I saw on the table, and the two sets of rules you're going to need:

enter image description here

enter image description here

Rules of Statue Park: (adapted from an earlier puzzle by @Deusovi)

  • Shade some cells of the grid to form the given set of pieces (here, the numbers 1, 2, 3 and 4, and a decimal point). Pieces may be rotated or reflected.
  • Pieces cannot be orthogonally adjacent (though they can touch at a corner).
  • All unshaded cells must be (orthogonally) connected.
  • Any cells with black-background dice must be shaded; any cells with white-background dice must be unshaded. Red-background dice provide no information for this puzzle and can be treated from the outset as blank spaces whose status needs to be determined.

Rules of Fillomino: (adapted from Nikoli)

  • Fill in all empty cells with numbers under the following rules. All dice (black, white and red) provide known numbers for this puzzle.
  • Numbers should be grouped together into 'blocks' of orthogonally connected cells in which each cell contains the same number.
  • The total number of cells making up each 'block' equals the value they all share (e.g. a block of two 2's, three 3's, etc.).
  • Different 'blocks' of the same size and value cannot border each other, horizontally or vertically (but may touch at a corner).

TASK: Solve the two small grid deduction puzzles (use the white grid only - not the grey) to help me work out what game we're playing tonight! Almost all of the Yahtzee scorecard text is irrelevant, although I'm led to believe the part my friend has circled may be important... Please explain the key logical steps leading to your solution.

A .xlsx version of the image with numbers in place of dice is available via filedropper.com.

Chain Puzzles are a novel approach to puzzle series creation, in which the solver of the previous puzzle in the chain becomes the setter of the next.

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    $\begingroup$ Note: All are welcome to discuss this puzzle, the series, its rules, and future suggestions for themes in the dedicated chatroom :) $\endgroup$ – Stiv Oct 28 '20 at 23:08
  • $\begingroup$ Can you clarify what you mean by "Fill each block with the same number horizontally or vertically."? What does it mean to fill a block with a number horizontally, or vertically? $\endgroup$ – msh210 Oct 28 '20 at 23:41
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    $\begingroup$ @msh210 (It's the Nikoli wording - best to take a look at the link for an example.) In a nutshell, every cell needs a number. These numbers should be organised into 'blocks' of orthogonally connected cells in which each cell has the same number and the total number of cells making up the block equals the value they all share. A block cannot border another block with the same value (horiz. or vertic.). I'll try alter the instruction wording in the morning. Hope this is clearer! $\endgroup$ – Stiv Oct 29 '20 at 0:07

I rotated the grid 90 degrees clockwise before solving the grid deductions, in order to reduce vertical space.

Let's solve Statue Park first.

First thing to note is that the 2 must be placed sideways, spanning rows 2 and 3 or 3 and 4, in order to keep the white cells connected. Then there are only two ways to place the 2:

In either case, the 4 and 3 are confined to a 5x7 space, and the 3 needs to be placed at the left or right end vertically. But if we place 2 on the left, the 3 at the right end will block off a white cell. Therefore we need to place the 2 on the right instead, and 3 on the left end of the board.

Now, both of the central two dots must be part of the 4, and there's only one way to place it without blocking some white cells:

And then the placement of the 1 and the dot is fairly obvious.

Now to the Fillomino.

Look at the 2 at R1C8. It can't extend neither left nor down, since it will form a too large area for a 2. Therefore it goes to the right. The same logic solves the upper right corner.

Both 5 and 6 should extend to the left due to their areas.

Now look at the lower left corner. The 6 must escape the corner, then the 3 at R5C5 cannot touch the surrounding 3's (too far away).

Starting with the confined 3 at R3C4, some easy deduction solves most of the left side. The 3 on the left should turn right, so that the remaining 3 cells can be filled with a 1 and two 2's, without the new 1 touching existing 1's.

Now look at the center 4's. They can't form two disjoint areas, so they must be connected. Also, R2C8 (surrounded by 1, 2, 2, 4) can't be a 1-island, so it must be part of 4. The 2 at R3C8 cannot extend to the left, since otherwise we can't fill the size-3 island.

Finally, the 6's must be connected, and it leaves a single possibility to fill in the rest:

Now that the two grids are solved, we can combine them in two ways:

One by keeping the numbers (Fillomino) on black cells (Statue Park), and the other by erasing them and keeping the rest of the numbers.

Turns out that the second interpretation is correct, and the column sums are

19 15 18 18 25

which spells out...


As @oAlt noticed, the friend already gave you the answer twice:

My friend - our host - was very apologetic...

"Ah, we're playing Yahtzee then!" I exclaimed. "No, SORRY," said my friend.

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    $\begingroup$ (oh, and the flavor text sneakily hints to the answer as well) $\endgroup$ – oAlt Oct 29 '20 at 1:44
  • $\begingroup$ Very nice, well done :) That is indeed the answer. Genuinely fascinated that you solved the statue park by placing the 2 and 3 first - I had designed it so there is only 1 place the 4 could possibly fit, but clearly in a grid so small there are (slightly) longer alternative deductive routes that will bring you to the answer too :) +1 and a green checkmark on its way... $\endgroup$ – Stiv Oct 29 '20 at 7:50
  • $\begingroup$ @Stiv 2 has a rotational symmetry and some funkiness in its shape, heavily restricting how it can be placed at all. On the other hand, 4 has eight different orientations and looked quite permissive to me, so I went ahead with 2. Btw, I just realized that there are three ways to place the 2 (at the same region as the first but the shape mirrored), and I could "cheat" by using the uniqueness argument :P $\endgroup$ – Bubbler Oct 29 '20 at 7:59

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