See more discussion of the puzzles from the United States’ 2021 Puzzle Grand Prix on this post. Note there are some construction details and potential spoilers on that post so view it after you solve.

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between a composite mode for line/edge drawing and a letter entry mode.)

Author/Opus: This is the 353rd puzzle from our managing editor Serkan Yürekli.

Rules: Standard Pentominous rules. Also, some circle clues are given in the grid which must be at the center of symmetry for a rotationally-symmetric pentomino shape.

Difficulty: 2.5 stars (estimate based off competition points; timing standards not available from our usual testers)

Solution: PDF

Note: Follow this link for other Pentominous puzzles. If you are new to this puzzle type, here are our easiest Pentominous to get started on. More Pentominous puzzles can be found in the Plenty o’ Pentominous series by Grant Fikes and Murat Can Tonta and in our beginner-friendly collection Intro to GMPuzzles by Serkan Yürekli.

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between a composite mode for line/edge drawing and a shading mode.)

Theme: Double Ring

Author/Opus: This is the 392nd puzzle from Thomas Snyder, aka Dr. Sudoku.

Rules: Variation of Spiral Galaxies. In addition to the standard rules, some circles are shaded gray and must belong to galaxies containing two gray circles, not one, with the circles in rotationally symmetric spots for those galaxies.

Difficulty: 4.5 stars

Time Standards (highlight to view): Grandmaster = 7:00, Master = 13:15, Expert = 26:30

Solution: PDF; a solution video is also available here.

Note: Follow this link for classic Spiral Galaxies puzzles on this website and this link for variations on Spiral Galaxies puzzles. If you are new to this puzzle type, here are our easiest Spiral Galaxies Puzzles to get started on. More Spiral Galaxies can be found in The Art of Puzzles 2.

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between a composite mode for line/edge drawing and a shading mode.)

Author/Opus: This is the 84th puzzle from our contributing puzzlemaster John Bulten.

Rules: Standard Spiral Galaxies rules. Also, there may not be four consecutive cells that are part of a galaxy in any row or column.

Difficulty: 3.5 stars

Time Standards (highlight to view): Grandmaster = 4:00, Master = 6:30, Expert = 13:00

Solution: PDF; a solution video is also available here.

Note: Follow this link for classic Spiral Galaxies puzzles on this website and this link for variations on Spiral Galaxies puzzles. If you are new to this puzzle type, here are our easiest Spiral Galaxies Puzzles to get started on. More Spiral Galaxies puzzles can be found in The Art of Puzzles 2.

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between a composite mode for line/edge drawing, a shading mode, and a shape (star) entry mode for the relay puzzle.)

Theme: Logical

Author/Opus: This is the 37th puzzle from our contributing puzzlemaster Carl Worth.

Rules: First, solve the top grid puzzle as a Mirror Universe puzzle: Divide the grid along the indicated lines into connected regions – “galaxies” – so that every cell is part of one galaxy and every galaxy has one circle clue inside it. If the galaxy contains a plain circle without any lines, the galaxy must be rotationally symmetric with that circle being the center of rotational symmetry. If the galaxy contains a circle with a horizontal, vertical, or diagonal line, the galaxy must have mirror symmetry when reflecting across the line given in the circle. Also, some cells contain black dots – “asteroids” – which must be symmetrically arranged based on the rules of symmetry (rotational or mirror) for every galaxy that contains them.

Mirror Universe + Asteroids Example by Carl Worth:

Then, copy all ten of the galaxy regions from the solved Mirror Universe into the bottom grid. Solve this puzzle as a Star Battle puzzle with two stars in every row, column, and region.

Answer String: For each row from top to bottom, enter the number of the first column from the left where a star appears. Enter these numbers as a single string with no separators.

Time Standards (highlight to view): Grandmaster = 8:00, Master = 10:15, Expert = 20:30

Solution: PDF

Note: Follow this link for other classic Star Battles. If you are new to this puzzle type, here are our easiest Star Battles to get started on. More Star Battle puzzles can be found in The Art of Puzzles and in our beginner-friendly collection Intro to GMPuzzles by Serkan Yürekli.

This week we are sharing easy sample puzzles from our ebook The Puzzlemasters’ Workshop which showcases six authors exploring new puzzle styles or variations with 8-10 challenges in each section. Today’s post is Mirror Universe.

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between an edge mode, a line mode, and a shading mode.)

Theme: Circle

Background: Variation of the region division puzzle Spiral Galaxies, with new clues indicating galaxies with mirror symmetry. This variation was created by Carl Worth.

Rules: Divide the grid along the indicated lines into connected regions – “galaxies” – so that every cell is part of one galaxy and every galaxy has one circle clue inside it. If the galaxy contains a plain circle without any lines, the galaxy must be rotationally symmetric with that circle being the center of rotational symmetry. If the galaxy contains a circle with a horizontal, vertical, or diagonal line, the galaxy must have mirror symmetry when reflecting across the line given in the circle.

Example by Carl Worth:

(No official times or solution entry for this week; just click “SOLVE?” when finished.)

Solution: Last page of PDF

Note: More Mirror Universe puzzles can be found in The Puzzlemasters’ Workshop.

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between a composite mode for line/edge drawing and a number entry mode.)

Theme: Clue Symmetry and Logic

Author/Opus: This is the 36th puzzle from our contributing puzzlemaster Carl Worth.

Rules: Combination of Spiral Galaxies and Fillomino rules. Divide the grid along the dotted lines into regions, each of which must contain either exactly one circle, or one or more identical given numbers. (Note that there are no “hidden polyominoes” in this puzzle meaning there are no regions without a given number or a given circle.) Each region containing a circle is a “galaxy” and must have rotational symmetry with the circle at its center. Each region with given numbers must be the same size in cells as those numbers. Two regions with numbers of the same size cannot share an edge, but a region with numbers and a region with a circle in it can be the same size.

Answer String: For each cell in the marked rows, enter the area of the region it belongs to. Enter just the last digit for any two-digit number. Start with the 4th row, followed by a comma, followed by the 8th row.

Time Standards (highlight to view): Grandmaster = 7:00, Master = 13:45, Expert = 27:30

Solution: PDF

Note: Follow this link for classic Spiral Galaxies puzzles on this website and this link for variations on Spiral Galaxies puzzles. If you are new to this puzzle type, here are our easiest Spiral Galaxies Puzzles to get started on. More Spiral Galaxies puzzles can be found in The Art of Puzzles 2.

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between a composite mode for line/edge drawing and a shading mode.)

Theme: Logical

Author/Opus: This is the 287th puzzle from our contributing puzzlemaster Grant Fikes.

Rules: Standard Spiral Galaxies rules. Then shade some dominoes (two-cell connected blocks) so that no two dominoes share an edge and so that every “galaxy” in the solved puzzle contains exactly two shaded cells.

Answer String: Enter the total number of horizontal dominoes (i.e., dominoes with two cells in the same row) in each row, starting at the top and proceeding to the bottom.

Time Standards (highlight to view): Grandmaster = 4:15, Master = 6:30, Expert = 13:00

Solution: PDF

Note: Follow this link for classic Spiral Galaxies puzzles on this website and this link for variations on Spiral Galaxies puzzles. If you are new to this puzzle type, here are our easiest Spiral Galaxies Puzzles to get started on. More Spiral Galaxies puzzles can be found in The Art of Puzzles 2.

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between a composite mode for line/edge drawing and a shading mode.)

Theme: Logical

Author/Opus: This is the 43rd puzzle from our contributing puzzlemaster Palmer Mebane.

Rules: Combination of Tetromino/object placement and Spiral Galaxies puzzle styles. Place the seven tetromino shapes into the grid, rotations allowed but not reflections. Tetrominoes do not touch each other not even diagonally and they do not cover any cell with part of a white circle. Digits on the left/top of the grid indicate the number of cells used by tetrominoes in that row/column. Digits on the right/bottom indicate the number of different tetromino shapes partially in that row/column. All remaining white cells must be part of connected regions – “galaxies” – with rotational symmetry. Each galaxy must have exactly one circle at its center of rotational symmetry.

Answer String: For each cell in the marked rows, enter the tetromino shape (as a capital letter IJLOSTZ) or the galaxy size in cells (enter just the last digit for any two-digit number). Separate the rows with a comma. An example answer would be “772TTT44SS,6664333LLL”.

Time Standards (highlight to view): Grandmaster = 4:45, Master = 9:30, Expert = 19:00

Solution: PDF; a solution video is also available here.

Note: Follow this link for classic Spiral Galaxies puzzles on this website and this link for variations on Spiral Galaxies puzzles. If you are new to this puzzle type, here are our easiest Spiral Galaxies Puzzles to get started on. More Spiral Galaxies puzzles can be found in The Art of Puzzles 2.

(view directly for a larger image)

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between a composite mode for line/edge drawing and a shading mode.)

Theme: New Constellation

Author/Opus: This is the 56th puzzle from our contributing puzzlemaster John Bulten.

Rules: Variation of Spiral Galaxies. In addition to the standard rules, some circles are shaded gray and must belong to galaxies containing two gray circles, not one, with the circles in rotationally symmetric spots for those galaxies.

Answer String: Enter the number of cells in each connected group (between bold lines) in the marked columns. Separate each column’s entry from the next with a comma. The example (using rows) has the answer “52,11131”.

Time Standards (highlight to view): Grandmaster = 2:15, Master = 3:30, Expert = 7:00

Solution: PDF

Note: Follow this link for classic Spiral Galaxies puzzles on this website and this link for variations on Spiral Galaxies puzzles. If you are new to this puzzle type, here are our easiest Spiral Galaxies Puzzles to get started on. More Spiral Galaxies puzzles will soon be found in The Art of Puzzles 2.

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between a composite mode for line/edge drawing and a shading mode.)

Theme: Double Spiral Galaxy (the pattern of galaxies is a double spiral as shown here)

Author/Opus: This is the 25th puzzle from our contributing puzzlemaster Carl Worth.

Rules: Variation of Spiral Galaxies. In addition to the standard rules, some circles are shaded gray and must belong to galaxies containing two gray circles, not one, with the circles in rotationally symmetric spots for those galaxies.

Answer String: Enter the number of cells in each connected group (between bold lines) in the marked rows. Separate each row’s entry from the next with a comma. The example has the answer “52,11131”.

Time Standards (highlight to view): Grandmaster = 10:30, Master = 17:00, Expert = 34:00

Solution: PDF

Note: Follow this link for classic Spiral Galaxies puzzles on this website and this link for variations on Spiral Galaxies puzzles. If you are new to this puzzle type, here are our easiest Spiral Galaxies Puzzles to get started on. More Spiral Galaxies puzzles will soon be found in The Art of Puzzles 2.