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The following grids can be solved using either Cave or Tapa rules. First, determine what kind of puzzle each grid represents. (They can both be of the same kind, or there could be one of each kind.) Then, solve each grid using the rules assigned to each grid.

Additionally, in each grid, there is a cell labeled ?, which represent a positive integer. The integer in Grid 1 is strictly greater than the integer in Grid 2, and they should be chosen so that there is a unique solution to both grids.

gdd_cave-tapa

Rules of Cave1

  • Shade some cells in the grid. Cells containing numbers cannot be shaded.
  • Groups of shaded cells must be connected to an edge of the grid i.e. there are no groups of shaded cells completely in the interior.
  • All unshaded cells must be orthogonally connected to one another.
  • Each numbered cell indicates the number of unshaded cells that are connected orthogonally to the cell, including the cell itself.

Rules of Tapa2

  • Shade some cells in the grid. Cells containing numbers cannot be shaded.
  • All shaded cells must be orthogonally connected to one another without forming a 2x2 square anywhere.
  • Each numbered cell indicates the length of consecutive shaded cells in the cells surrounding it.
  • If there is more than one number in a cell, then there must be at least one unshaded cell separating the groups of shaded cells.

1 Paraphrased from the rules of Grandmaster Puzzles
2 Paraphrased from the rules of Grandmaster Puzzles

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  • $\begingroup$ May I have an explanation for the downvote here? Would appreciate it to make my future puzzles better :) $\endgroup$ – HTM Nov 4 at 0:39
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Grid 2 can be quickly deduced to not be a Tapa - if we fill the cells per Tapa rules for the the 3 in r5c1 and the 3 in r2c1 we get a filled 2x2 above them. We can then continue to solve it as a Cave and we find the following solution. It is not necessary to determine what the question mark is in advance and from the finished solution we find that it is 5.
Solution to grid 2
Grid 1 is not a cave, but I did not record the step by step conclusion for that, it took me a little longer, but there was a problem connecting the 2 in r2c5 to the rest of the cave. So we proceed to solve as a Tapa. We know that the middle digit is 6 or more. We get to this situation:
Progress on Grid 1
I went with trial and error, if we assume the ? number to be 6 there are two solutions with r1c3 either shaded or unshaded. With 7 there are even more. 8 Produces a unique solution to the grid:
Solution for Grid 1

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  • $\begingroup$ Looks pretty good! I accepted your answer, but to make this a fully complete answer, would appreciate it if you could include your working out of Grid 2 as well as deducing what kind of puzzle Grid 1 is. $\endgroup$ – HTM Nov 1 at 5:49

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