Triplets by Palmer Mebane

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 Triplets.

Triplets by Palmer Mebane

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Theme: Clue Symmetry and Logic

Background: An original number placement puzzle created by Palmer Mebane.

Rules: Fill each cell with a number so that all 27 three-digit numbers with digits 1, 2, or 3 are used exactly once. For each pair of cells sharing a side, the two numbers in those cells must have equal digits in exactly two of the three positions (ones, tens, or hundreds).

Example by Palmer Mebane:

Triplets by Palmer Mebane

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

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

Pyramid by Palmer Mebane [bonus]

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Pyramid by Palmer Mebane

Theme: Good Odds

Author/Opus: This is the 49th puzzle from our contributing puzzlemaster Palmer Mebane.

Rules: Place a digit from 1 to 9 into each empty cell so that, for each row above the bottom row, every digit is the sum or difference of the two digits immediately below it. Rows marked in gray cannot have repeated digits; rows in white must have at least one repeated digit.

Also see this example:

Gaps Between Battleships Example by Thomas Snyder

Answer String: Enter the digits in the marked rows from left to right, separating each row with a comma.

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

Skyscrapers (with Sum Baskets) by Palmer Mebane

Skyscrapers (with Sum Baskets) by Palmer Mebane

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Theme: Fours and Fives

Author/Opus: This is the 48th puzzle from our contributing puzzlemaster Palmer Mebane.

Rules: Standard Skyscrapers rules (using digits 1 to 7). Also, there are some regions (”Sum baskets”) in the grid marked by dashed lines. The sum of the buildings in these sum baskets is given. Building heights can repeat within a basket.

Answer String: Enter the 1st row from left to right, followed by a comma, followed by the 7th row from left to right.

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

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

Inner Coral by Palmer Mebane

Inner Coral by Palmer Mebane

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Theme: Clue Symmetry and Logic

Author/Opus: This is the 47th puzzle from our contributing puzzlemaster Palmer Mebane.

Rules: Shade some empty cells black to create a single connected wall (the “Coral”). The shaded cells cannot form a 2×2 square anywhere in the grid, and all unshaded cells including clue cells must be connected to an edge of the grid. Clues in the gray cells indicate the lengths of the first shaded segments visible from this cell in all four directions (clues are given in ascending order). [For clarity, when considering the “first shaded segment” in a direction, gray cells see through all empty and gray cells to the edge of the grid when finding this segment, if any.]

Also see this example:

Inner Coral Example by Thomas Snyder

Answer String: Enter the length in cells of each of the shaded segments from left to right for the marked rows, starting at the top. Separate each row’s entry from the next with a comma.

Time Standards (highlight to view): Grandmaster = 4:30, Master = 8:00, Expert = 16:00

Editorial Note: Many solvers can confuse Coral with another puzzle type with similar spelling. An easy way to remember the difference is that Cave has no R’s and also has no 2×2 Region constraint. Coral puzzles, with an R, do have this region constraint. The other general rules (about not enclosing white spaces and having a single shaded group) are shared between Cave and Coral puzzles.

Skyscrapers (with Mirrors) by Palmer Mebane

Skyscrapers (with Mirrors) by Palmer Mebane

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Theme: Logical

Author/Opus: This is the 46th puzzle from our contributing puzzlemaster Palmer Mebane.

Rules: Variation of Skyscrapers. Insert a digit from 1 to 5 into each empty cell so that each row and column has one copy of each digit and exactly one mirror. Each digit in the grid represents the height of a building, and clues on the outside of the grid indicate how many buildings can be “seen” when looking from that direction, including those seen through the mirror’s reflection. Buildings block the view of any building with equal or lower height behind them.

Also see this example:

Skyscrapers (with Mirrors) by Thomas Snyder

Answer String: Enter the 1st row from left to right, followed by a comma, followed by the 6th row from left to right. Ignore the cells with the mirrors when entering the solution (i.e., just enter cells with digits 1-5).

Time Standards (highlight to view): Grandmaster = 4:45, Master = 7:00, Expert = 14:00

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

Skyscrapers (Battleships) by Palmer Mebane

Skyscrapers (Battleships) by Palmer Mebane

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Theme: Logical

Author/Opus: This is the 45th puzzle from our contributing puzzlemaster Palmer Mebane.

Rules: Combination of Skyscrapers and Battleships. Place the indicated fleet into the grid so that ships do not touch each other not even diagonally. The size of the ship represents its height as in a Skyscrapers puzzle, and the clues outside the grid indicate how many ships are visible in that direction. Ships block the view of any ship of equal or smaller size behind them.

Answer String: For each row from top to bottom, enter the number of the first column from the left where a ship segment appears (enter just the last digit for any two-digit number). If the row is empty, enter 0. Enter these numbers as a single string with no separators.

Time Standards (highlight to view): Grandmaster = 3:45, Master = 8:00, Expert = 16:00

Note: Follow this link for classic Skyscrapers puzzles and this link for more classic Battleships puzzles.

Skyscrapers (with Mirrors) by Palmer Mebane

Skyscrapers (with Mirrors) by Palmer Mebane

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Theme: All For One, …

Author/Opus: This is the 44th puzzle from our contributing puzzlemaster Palmer Mebane.

Rules: Variation of Skyscrapers. Insert a digit from 1 to 5 into each empty cell so that each row and column has one copy of each digit and exactly one mirror. The direction of the mirrors must also be determined. Each digit in the grid represents the height of a building, and clues on the outside of the grid indicate how many buildings can be “seen” when looking from that direction, including those seen through the mirror’s reflection. Buildings block the view of any building with equal or lower height behind them.

Also see this example:

Skyscrapers (with Mirrors) by Thomas Snyder

Answer String: Enter the 3rd row from left to right, followed by a comma, followed by the 5th row from left to right. Use the slash characters / or \ to enter the mirrors.

Time Standards (highlight to view): Grandmaster = 2:45, Master = 6:00, Expert = 12:00

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