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Inspired by the "Treasure Hunter Monolith" minigame from Danganronpa V3


Dodgy Dies Guide


Terminology

Block - a single die on the grid.

Cycle - a list of blocks

Value - the position of a block in the cycle.

Group - a collection of (at least two) same valued blocks which are positioned so that they form an overall structure. For a block to be included in the structure it must be adjacent to another block in the structure. The structure is considered as one entity and always includes every block that can legally exist as part of the structure.

Move - the elimination of a group from the grid, causing all adjacent blocks to increase in value.

Rules

In this puzzle you will be presented with a grid of blocks. Your goal is to eliminate all blocks so that no block remains on the grid - in the fewest moves possible. For each move you get to pick a group that is currently on the grid and eliminate it. All blocks that are currently adjacent to the eliminated group will then increase in value. The values loop so a block with the highest value will change into the lowest value block. A block with a cross is immune to changing value however all other rules still apply (i.e. can still be eliminated and can exist in a group). Clues for the solution will be given in the puzzle, your answer must satisfy those clues.

Examples

These examples will use this cycle: four dies in a row White (1), Red (2), Yellow (3), Blue (4) --> White (1)...

The groups available in this example grid have been highlighted red lines around blocks Here is an example of elimination! The highlighted group in the left grid is eliminated and the grid transforms into the grid on the right two similar grids

Dodgy Dies: The Puzzling Premiere


The cycle for this puzzle is: four dies in a row White (1), Red (2), Yellow (3), Blue (4) --> White (1)...

Eliminate all blocks from this grid grid of blocks

Clues

  • 21 White (1) blocks are eliminated
  • 15 Red (2) blocks are eliminated
  • 29 Yellow (3) blocks are eliminated
  • 45 Blue (4) blocks are eliminated
  • 2 crossed blocks are present
  • There is something 'special' about the solution. Perhaps I'm making you work towards something?

Hints

Hint 1

Jigsaw strategy?

Hint 2

An unimaginable number of moves are possible. The clues and rules won't help you in this regard. However, there is a small amount of something else that can guide you towards the answer!

Hint 3

The number of moves used for the solution is between (but not excluding) 12 and 16! I wonder if anything new can be learned from this information...

Hint 4

All eliminated Red (2) blocks are adjacent to other eliminated Red (2) blocks. This hint is powerful but be careful; the wrong conclusion may fool you!

Hint 5

The eliminated blocks at every corner of the grid are Blue (4). The remaining eliminated Blue (4) blocks are all adjacent to other eliminated Blue (4) blocks! Just like in hint 4, be extra careful with your reasoning!

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  • 1
    $\begingroup$ At first glance, I don't see a nice way to deduce anything logically - I could be missing something, but I'm not sure grid-deduction really applies here? $\endgroup$ – Deusovi Aug 15 at 21:26
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    $\begingroup$ Do "groups" have to be maximal connected sets of same-value dice? E.g., are we allowed to take just the bottom-right die as a "group" and eliminate it, or if we do that do we have to take the other 5 that it's together with? $\endgroup$ – Gareth McCaughan Aug 15 at 21:36
  • 1
    $\begingroup$ Do the counts of eliminated blocks refer to what sort of blocks they are when eliminated or what sort of blocks they are at the beginning? $\endgroup$ – Gareth McCaughan Aug 15 at 21:36
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    $\begingroup$ Actually, I think I can answer my own question about the counts: since they don't perfectly match the block-counts in the initial position and everything's meant to end up eliminated, they must refer to what the blocks are immediately before their elimination, right? $\endgroup$ – Gareth McCaughan Aug 15 at 21:40
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    $\begingroup$ I can't get past the use of "dice/dices". The singular is "die"; the plural is "dice". $\endgroup$ – shoover Aug 15 at 22:58
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Okay, this was worth persisting with! It's hard to spot exactly where to start without some trial and error, and it's very hard to explain the logical steps retrospectively since a lot of it is a case of "Well, that didn't work... how about this instead...?" but the final solution is very satisfying...

Note that in the diagrams that follow I have converted all dice to coloured digits 1-4. A black zero implies a piece has been eliminated. The two 4's with crosses in the original diagram are represented here with thick black edges - their values will never change due to the stated rules.

Firstly:

Moves 1-4: Note the hint to follow a 'jigsaw strategy' - this implies we should be starting with the edge pieces. Immediately we can take out the top left and bottom right corners so that their adjacent dice all now change number to become part of a larger group. However, before taking out the remaining two corners, it would be helpful to remove the two tetronimoes in the top (1's) and bottom (2's) rows...

Moves 5-6: Now remove the bottom left corner 4's, but leave the ones in the top right for now (we want to turn those adjacent 3's to 4's first, ideally). Also, eliminate the 4's in the top left, creating a large bank of 3's.

Move 7: Remove that bank of 3's. This will convert that 2 near the top into a 3, the 4 below it into a 1, and the adjacent 1's will join a bank of 2's.

Move 8: Eliminate the bank of 3's at the top.

Move 9: Eliminate the large bank of 1's towards the right-hand side. This leaves an isolated group of 4's and an isolated group of 3's on the right, which will be eliminated next.

enter image description here

Next:

Moves 10-12: Eliminate the two groups formed by the last turn, and also the group of 2's on the left.

Move 13: Eliminate the remaining 1's, converting all adjacent 3's to 4's. (The adjacent 4 with the black edges is unaffected, remember...)

Move 14: Take out those 4's to leave just a block of three 4's and a block of two 3's.

Moves 15-16: Finally, remove the 4's first, then the 3's (which have become 4's) - the grid is now fully eliminated! (And within the number of moves stated in Hint 3 - a useful confirmation.)

enter image description here

And what do we note by looking at the dice values at the point when they were each eliminated? Well:

The resulting pattern bears a striking resemblance to the Puzzling Stack Exchange logo, don't you think?!

Feedback for the OP, as requested:

It was pretty difficult to deduce the answer to this logically - it really was a case of trial and error until dead ends were reached, although some deductions could be made by spotting that when adjacent numbers differed by 1 it was likely that the lower number had to be removed before the higher one. As for the hints, I didn't use 2, 4 or 5 at all, although 4 or 5 made for useful double-checking at the end. I enjoyed it though - nice puzzle! :)

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  • $\begingroup$ Great work and well done for persisting with this even if it was a rough test run! I did analyse the puzzle and along the way I did encounter a couple of branching paths however I thought that clues (so that the solver would have a general idea of what they were working towards) and a good analysis by the solver would be enough - I was possibly biased or made an assumption at some point which damaged the integrity of the puzzle. Your feedback is appreciated! If I ever return to this I'll make more condensed puzzles and I will ensure that only definitive, pure logic is necessary $\endgroup$ – Adam Oct 31 at 0:33
  • $\begingroup$ Oh and it is disappointing that I can't give you the original bounty... so here is a new one, congrats! $\endgroup$ – Adam Oct 31 at 0:40
  • $\begingroup$ Aw, thanks :) I think in general it's hard to plan a perfectly logical solution for an elimination puzzle when there are hundreds of potential ways to reach dead ends, as often you can't tell if you made the right move til five or six turns later. The trial and error process is probably vital - I wouldn't worry too much about removing that entirely. You probably don't want to get bigger than this size though - might become impossibly hard! $\endgroup$ – Stiv Oct 31 at 7:41
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New Solution

45 in 8 steps

enter image description here

Old solution

Obviously, this is a long solution, but I hope this can be of help to other answerers.

Steps 1-8:

enter image description here

Steps 9-16:

enter image description here

Steps 17-24:

enter image description here

Steps 25-29:

enter image description here

The remaining gets trivial and requires 8 more steps, rendering the solution using

a disappointing 37 steps.

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  • 3
    $\begingroup$ You can't remove single blocks, so this doesn't work at all. $\endgroup$ – Deusovi Aug 31 at 4:18
  • $\begingroup$ oops sorry, will try to improve on it... $\endgroup$ – Omega Krypton Aug 31 at 4:23
  • $\begingroup$ The current attempt is very good so far! $\endgroup$ – Adam Aug 31 at 15:02

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