Puzzles on this page are at the difficult end of the scale. Take your time with them and always feel free to email us to ask for a nudge. If you do, a screenshot of your current progress will be very helpful! Puzzles are added in reverse chronological order so newer puzzles are at the top.

Yes, we're back to modular lines! And still playing with hidden modular lines under different constraints. This puzzle also appears in Heartburn Collection 1.

Estimated difficulty: 3,5/5

*Rules*

Standard sudoku rules apply: every row, column, and box must contain a complete set of the digits 1-9.

Modular lines: every set of three sequential digits along a line must contain a complete set of residues modulo 3, i.e. one digit from {1,4,7}, one from {2,5,8}, and one from {3,6,9}. Digits may repeat on a line if allowed by other rules.

Sandwich sums: numbers outside the grid indicate the sum of all cells between 1 and 9 in that row or column, excluding 1 and 9 from the sum.

Every sandwich, including the crust, forms a hidden modular line. For example, a sandwich clue of 8 could be made of the three cells 189 but could not be 1269.

A collection of constraints with interesting interactions. We started this puzzle and set it aside for a while, finally adding an extra clue to make it more fun.

Estimated difficulty: 3.5/5

*Rules*

Normal sudoku rules apply. Each row, column, and box must contain a complete set of the digits 1-9.

Normal killer cage rules apply: digits in cages cannot repeat and must sum to the number shown in the upper left corner of the cage.

Digits along a thermometer must strictly increase from bulb to top but do not have to be consecutive.

Green lines are German whispers lines. Adjacent digits along the line must differ by 5 or more.

Purple lines are Renban lines. Digits along a renban line form a set of consecutive digits in any order.

Despite the plethora of thermometers, this is a rather difficult puzzle requiring advanced solving techniques for the break-in. This puzzle also appears in the Heartburn Collection.

Estimated difficulty: 3.5/5

*Rules*

Normal sudoku rules: every row, column, and box must contain a complete set of the digits 1-9.

Digits on thermometers must increase from bulb to tip.

Our first collaborative set with BremSter, this delightful puzzle was featured on Cracking the Cryptic on 22 October 2022.

Estimated difficulty: 3.5/5

*Rules*

Normal sudoku rules apply: every row column and 3x3 box must contain a complete set of the digits 1 through 9.

Digits connected by an X sum to 10. Digits connected by a V sum to 5. Not all Xs or Vs are necessarily given.

Digits along a purple renban line form a set of non-repeating consecutive digits in any order.

Any set of three contiguous cells along a beige entropic line must contain one low digit (123), one medium digit (456), and one high digit (789).

Yes. The grid is empty. This puzzle was a collaboration with Crusader175 building on some of the ideas from Cross About Dominoes. This puzzle also appears in the Heartburn Collection.

Estimated difficulty: 4/5

*Rules*

Normal sudoku rules apply: every row, column, and box contains a complete set of the digits 1-9.

The finished grid contains the minimum number of friendly cells, i.e. cell that contain digits which match at least one of the row, column, or box number.

Every diagonal of length 7 or more is either an entropic line or an isotropic line. On entropic lines, every set of three sequential digits must contain a low digit (1,2,3), a middle digit (4,5,6), and a high digit (7,8,9). On isotropic lines, all digits are from the same entropic rank (low/middle/high).

Each cell is orthogonally adjacent to at least one cell whose digit has a difference of at least 4 with the digit in the original cell.

Solve in the __Sudokupad app__ with solution checker

This puzzle was initially published in the Modular Lines Competition Pack for Cracking the Cryptic. It is republished here with permission from CtC. The complete pack is available to CtC Patreon members. This puzzle was the genesis for our later puzzle, Cross About Dominoes, that was featured on Cracking the Cryptic.

Estimated difficulty: 3.5/5

*Rules*

Normal sudoku rules apply.

Little killers: Numbers outside the grid give the sum of the digits along the indicated diagonal. Digits can repeat along the little killer diagonal if allowed by the other rules.

Modular lines: every set of three sequential digits along a line must contain a complete set of residues modulo 3, i.e. one digit from {1,4,7}, one from {2,5,8}, and one from {3,6,9}. Digits on two-cell lines cannot be from the same residue set. Digits may repeat on a line if allowed by other rules.

Unimodular lines: every digit along the line is from the same residue class modulo 3, i.e. all from {1,4,7} or all from {2,5,8} or all from {3,6,9}.

EVERY diagonal in the grid, including those marked as little killers, is either modular or unimodular. It is up to the solver to determine the nature of each diagonal.

Tea with the Queen was constructed in response to Mark's solve of Bastille Day. Since the fortress cells were causing trouble, we decided to add a negative constraint on fortresses, such that there were exactly nine fortress cells in the entire grid. We paired anti-fortress cells, which we think of as palace cells, with sandwich clues and wound up having Tea with the Queen. This puzzle also appears in the Heartburn Collection and we were delighted when it was featured by BremSter on 25 August 2022.

Estimated difficulty: 3.5/5

*Rules*

Standard sudoku constraints: each row, column, and box must contain a complete set of the digits 1-9.

Fortress cells: shaded cells are fortress cells and must be larger than any orthogonally adjacent unshaded cell. All fortress cells are shown. That is, there is a negative constraint on fortresses so every unshaded cell must be orthogonally adjacent to at least one larger digit.

Sandwich constraint: numbers outside the grid indicate the sum of all cells between 1 and 9 (excluding 1 and 9 from the sum) in that row or column.

Despite its apparent simplicity, this is easily the hardest puzzle we have set to date (as of July 2022). It requires lots of thought about the interplay of the disjoint constraint and the thermos.

Estimated difficulty: 4.5/5 (Indigestion-level)

*Rules*

Normal sudoku rules apply. Digits on thermometers must increase from bulb to tip but need not be consecutive (*standard thermometer constraint*). Additionally, each position in the 3x3 boxes contains a full set of the digits 1 to 9. In other words, no digit can show up in the same position in two different 3x3 boxes (*standard disjoint groups constraint*).

This puzzle was initially published in the Modular Lines Competition Pack for Cracking the Cryptic. It is republished here with permission from CtC. The complete pack is available to CtC Patreon members. .

Estimated difficulty: 4/5

*Rules*

Normal sudoku rules apply.

Modular lines: every set of three sequential digits along a line must contain a complete set of residues modulo 3, i.e. one digit from {1,4,7}, one from {2,5,8}, and one from {3,6,9}. Digits on two-cell lines cannot be from the same residue set. Digits may repeat on a line if allowed by other rules.

X-Sums: Numbers outside the grid give the sum of the first X digits in the row or column (starting next to the number outside the grid) where X is the first digit along that row or column.

Every X-sum forms a hidden modular line of length X.

This puzzle explores the interaction of modular lines with little killers.

Estimated difficulty: 3.5/5

*Rules*

Standard sudoku constraints: each row, column, and box must contain a complete set of the digits 1-9.

Standard little killers: Numbers outside the grid indicate the sum of the digits along the indicated diagonal. Digits may repeat along a little killer diagonal if allowed by other rules.

Modular Lines**:** Every set of three sequential digits along a line must contain a complete set of residues modulo 3, i.e. one digit from {1,4,7}, one from {2,5,8}, and one from {3,6,9}. Digits may repeat on a line if allowed by other rules.

Solve in the SudokuPad app with embedded solution check

We continue to play with the modular lines constraint in this puzzle.

Estimated difficulty: 4/5

*Rules*

Standard sudoku constraints: each row, column, and box must contain a complete set of the digits 1-9.

Modular Lines**:** Every set of three sequential digits along a line must contain a complete set of residues modulo 3, i.e. one digit from {1,4,7}, one from {2,5,8}, and one from {3,6,9}. Digits may repeat on a line if allowed by other rules.

Kropki dots: Digits on either side of a black dot are in a 2:1 ratio. Digits on either side of a white dot are consecutive. Not all dots are shown.

A precursor to Residual X-Rays, this puzzle was our first set using hidden modular lines.

Estimated difficulty: 3/5

*Rules*

Normal sudoku rules apply. Each row, column, and box must contain a complete set of the digits 1-9.

X-Sums: Digits outside the grid give the total of the first X digits in row or column, where X is the first digit along that row or column, starting with value outside the grid.

Every X-sum forms a hidden modular line of length X.

Modular lines: Every set of three sequential digits along a modular line must contain a complete set of residues modulo 3, i.e. one digit from {1,4,7}, one from {2,5,8}, and one from {3,6,9}.

The product of a sleepless night, this puzzle also appears in the Indigestion Collection.

Estimated difficulty: 3.5/5

*Rules*

Standard sudoku rules apply. Digits along an arrow sum to the number in the attached circle and may repeat if permitted by standard sudoku constraints (*standard arrow constraint*). Digits separated by a white dot form a consecutive pair. Digits separated by a black dot are in a 1:2 ratio (*standard kropki dot constraints*).

Find your way carefully into the swirling wind of constraints on this puzzle, which also appears in the Showcase.

Estimated difficulty: 3.5/5

*Rules*

Standard sudoku rules apply. Digits along an arrow must sum to the number in the connected circle and may repeat if permitted by normal sudoku rules (*standard arrow rules)*. Numbers outside the grid indicate the sum of all the digits along the diagonal indicated by the arrow (*standard little killer rules*). Digits can repeat along the diagonal if permitted by normal sudoku rules.

This was the first puzzle FullDeck ever set and it has a rather esoteric rule set since it was built specifically to showcase a particular mathematical idea: complete sum-free sets modulo 10. Knowledge of that mathematics is not necessary to solve the puzzle but email us if you need a hint. This puzzle has received "great puzzle," "ingenious puzzle," and "mind-blowing puzzle" reactions in the CTC Discord channels.

Estimated difficulty: 4/5

*Rules*

Normal sudoku rules apply. Digits on thermometers must increase from bulb to tip. Digits on purple lines are prime and can repeat along the line as long as they satisfy normal sudoku constraints.

Cages are sum-free modulo 10. That means that for any pair of numbers (including doubles) within the cage, the ones digit of their sum cannot be within the cage. For example, if 6 and 7 are in the cage, then neither 2, 3, nor 4 can be in the cage since 6 + 6 = 12, 6 + 7 = 13, and 7 + 7 = 14. Note that while the sum-free condition includes doubles, digits cannot repeat within a cage.

The rules to Three Is the Loneliest Number are a bit long but it's a great puzzle if you're already familiar with sandwich sums. It has received multiple "exceptional puzzle" and "beautiful logic" reactions from the CTC community.

Estimated difficulty: 4/5

*Rules*

Normal sudoku rules apply. Thermometers are strictly increasing from bulb to tip (*standard thermo constraint*). Numbers outside the grid indicate the sum of the digits between 1 and 9 in that row or column (*standard sandwich sum constraint*). Some sandwich sums are indicated by dashes and you must determine their value. However, each sandwich sum (whether indicated by a value or a dash) is a distinct prime number and those values increase from top to bottom and from left to right. Cells separated by a black dot are in a 3:1 ratio. Not all black dots in the grid are indicated. **NOTE:***The locations of the mystery sandwiches will not show up on the CTC app but they are in columns 4, 6, 8, and 9 and in rows 2, 5, 6, and 7.*

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