PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to shift between shading mode and the linex mode where left click+drag draws lines and right click marks X’s)

Theme: Clue Symmetry and Logic

Rules: Standard Cave rules.

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

Time Standards (highlight to view): Grandmaster = 1:30, Master = 2:15, Expert = 4:30

Solution: PDF

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

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; 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; use tab to alternate between a composite mode for line/edge drawing and a number entry mode.)

Theme: 28 Dice (Opus #6 in Grant’s series; also the first one with no border clues.)

Rules: Standard Fillomino rules.

Answer String: For each cell in the marked rows/columns, enter the area of the polyomino it belongs to. Start with the 6th column, followed by a comma, followed by the 10th column.

Time Standards (highlight to view): Grandmaster = 1:15, Master = 1:45, Expert = 3:30

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; use tab to alternate between a composite mode for line/edge drawing and a number entry mode.)

Theme: Lambda

Rules: Standard Fillomino rules.

Answer String: For each cell in the marked rows/columns, enter the area of the polyomino it belongs to. Start with the 7th row, followed by a comma, followed by the 6th column.

Time Standards (highlight to view): Grandmaster = 2:30, Master = 4:00, Expert = 8:00

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; 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). See an earlier Pentominous puzzle here.

Specifically, divide the grid into 45 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 marked rows from left to right, separating the rows with a comma. Use CAPITAL LETTERS!

Time Standards (highlight to view): Grandmaster = 6:30, Master = 10:30, Expert = 21:00

Solution: PDF

Note: Follow this link for other puzzles involving Pentominoes.

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to shift between shading mode and the linex mode where left click+drag draws lines and right click marks X’s)

Theme: Dominoes — in both the clues and the variation rules

Rules: Standard Cave rules. Also, the exterior of the cave (the cells not seen by the numbers) must be divisible into dominoes (1×2 rectangles) in at least one way.

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

Time Standards (highlight to view): Grandmaster = 4:15, Master = 9:00, Expert = 18:00

Solution: PDF

Note: Follow this link for other classic Caves. If you are new to this puzzle type, here are our easiest Cave Puzzles 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 number entry mode.)

Theme: 28 dice again: opus #5 in Grant’s series with just 28 “dice” givens.

Rules: Standard Fillomino rules.

Answer String: For each cell in the marked rows/columns, enter the area of the polyomino it belongs to. Start with the 5th row, followed by a comma, followed by the 6th row.

Time Standards (highlight to view): Grandmaster = 1:20, Master = 2:00, Expert = 4:00

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; use tab to shift between shading mode and the linex mode where left click+drag draws lines and right click marks X’s)

Theme: Lines

Rules: Standard Cave rules.

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

Time Standards (highlight to view): Grandmaster = 1:45, Master = 3:00, Expert = 6:00

Solution: PDF

Note: Follow this link for other classic Caves. If you are new to this puzzle type, here are our easiest Cave Puzzles 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.)

This is a “Twisted Tuesday” puzzle variation.

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 = 4:30, Expert = 9:00

Solution: PDF

Note: Follow this link for other puzzles involving Pentominoes.