Today’s surprise comes from Nikolai Beluhov, a graduate student of mathematical logic who has been sharing some creative puzzle ideas with me recently. Some of them have ended up on his new puzzle blog Puzzled By Titles. This puzzle has become a Sunday Surprise.

Much like a set of Matryoshka dolls, this Fillomino is a puzzle with many layers. Remove the outer border and a new valid Fillomino arises. Keep doing this all the way down to the very center where a 2×2 puzzle awaits. The layers have a wide variety of difficulty and required logical strategies. Can you solve them all?

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: Matryoshka (nesting property) across 5 puzzles

Rules: Standard Fillomino rules.

Answer String: For each puzzle from largest (10×10) to smallest (2×2), enter the numbers placed in each cell along the upper-left to lower-right diagonal in order. Separate each puzzle’s entry by a comma (Your answer will be of the form AAAAAAAAAA,BBBBBBBB,CCCCCC,DDDD,EE).

Solution: PDF

Note: Follow this link for other classic Fillomino and this link for more variations on Fillomino puzzles. If you are new to this puzzle type, here are our easiest Fillomino puzzles to get started on.

PDF

or solve online (using our beta test of Penpa-Edit tools)

Theme: Four-leaf Clover (Note: This puzzle was one of the qualifying round puzzles from this year’s Arlington Puzzle Festival)

Rules: Standard Sudoku rules.

Answer String: Enter the 1st row from left to right, followed by a comma, followed by the 9th row from left to right.

Time Standards (highlight to view): Grandmaster = 3:00, Master = 5:15, Expert = 10:30

Solution: PDF

Note: Follow this link for other classic Sudoku. If you are new to this puzzle type, here are our easiest Sudoku to get started on. More classic Sudoku puzzles can be found in The Art of Sudoku, The Art of Sudoku 2 and in our beginner-friendly collection Intro to GMPuzzles by Serkan Yürekli.

PDF

or solve online (using our beta test of Penpa-Edit tools)

Theme: Logical

Rules: Standard LITS rules.

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 = 1:15, Master = 2:00, Expert = 4:00

Solution: PDF

PDF

or solve online (using our beta test of Penpa-Edit tools)

Theme: Nothing Important

Rules: Standard TomTom rules, using digits from 1-6.

Answer String: Enter the 1st row from left to right, followed by a comma, followed by the 6th row from left to right.

Time Standards (highlight to view): Grandmaster = 5:15, Master = 8:00, Expert = 16:00

Solution: PDF

Note: Follow this link for other classic TomTom. If you are new to this puzzle type, here are our easiest TomTom to get started on.

PDF

or solve online (using our beta test of Penpa-Edit tools)

Theme: GM Puzzles

Rules: Standard Statue Park rules.

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 = 4:00, Master = 6:00, Expert = 12:00

Solution: PDF

Note: Follow this link for other Statue Park Puzzles. If you are new to this puzzle type, here are our easiest Statue Parks to get started on.

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.)

Theme: Logical

Rules: Variation of Fillomino rules where regions with the same shape must avoid each other instead of regions with the same size (all regions in a pentominous puzzle are pentominoes).

Specifically, divide the grid into 20 pentominoes so that no two pentominoes of the same shape (including rotations/reflections) share an edge. A cell with a letter in it must be part of the pentomino shape normally associated with that letter as given below the grid. Not all pentomino shapes need appear.

Answer String: Enter the letter associated with the pentomino occupying each cell in the two marked rows from left to right, separating the rows with a comma. Use CAPITAL LETTERS!

Time Standards (highlight to view): Grandmaster = 2:00, Master = 4:00, Expert = 8:00

Solution: PDF

Note: Follow this link for other puzzles involving Pentominoes.

PDF

or solve online (using our beta test of Penpa-Edit tools)

Theme: Logical (Note: This puzzle was one of the qualifying round puzzles from this year’s Arlington Puzzle Festival)

Rules: Standard Sudoku rules.

Answer String: Enter the 4th row from left to right, followed by a comma, followed by the 6th row from left to right.

Time Standards (highlight to view): Grandmaster = 2:00, Master = 2:45, Expert = 5:30

Solution: PDF

Note: Follow this link for other classic Sudoku. If you are new to this puzzle type, here are our easiest Sudoku to get started on. More classic Sudoku puzzles can be found in The Art of Sudoku, The Art of Sudoku 2 and in our beginner-friendly collection Intro to GMPuzzles by Serkan Yürekli.

PDF

or solve online (using our beta test of Penpa-Edit tools)

Theme: Triple Play

Rules: Standard Cross the Streams rules.

Answer String: Enter the length in cells of each of the black segments from top to bottom for the marked columns, going in order from A to B to C to D and separating each entry with a comma.

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

Solution: PDF

PDF

or solve online (using our beta test of Penpa-Edit tools)

Theme: Clipped Rectangles

Rules: Standard Star Battle rules. Two stars per 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 = 2:15, Master = 3:15, Expert = 7:00

Solution: PDF

Note: Follow this link for other classic Star Battles and this link for Star Battle variations. 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, in the book Star Battle by JinHoo Ahn, and in our beginner-friendly collection Intro to GMPuzzles by Serkan Yürekli.

PDF

or solve online (using our beta test of Penpa-Edit tools)

Theme: Windmill (Note: This puzzle was the Team USA contribution to the Sudoku Grand Prix Final recently held in Beijing)

Rules: Standard Even/Odd Sudoku rules (i.e., cells with a square contain an even digit; cells with a circle contain an odd digit).

Answer String: Enter the 5th row from left to right, followed by a comma, followed by the 5th column from top to bottom.

Time Standards (highlight to view): Grandmaster = 3:00, Master = 4:30, Expert = 9:00

Solution: PDF

Note: Follow this link for more Even/Odd Sudoku puzzles. If you are new to this puzzle type, here are our easiest Even/Odd Sudoku to get started on. More Even/Odd Sudoku puzzles can be found in The Art of Sudoku 2.