An easier modular lines puzzle that is perhaps just slightly above GAS difficulty. The "leftovers" refers to the uses of modularity, which is all about remainders. The "deadly" refers to the killer cages in the puzzle. This puzzle also appears in the GAS Collection.

Estimated difficulty: 1.5/5

*Rules*

Normal 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 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}.

Killer cages: Digits in cages marked by dashed lines cannot repeat and must sum to the total shown in the upper left corner of the cage.

When this puzzle was set, temperatures across the globe were hitting record extremes (high or low depending on location). It combines modular line logic with thermometers. This puzzle also appears in Indigestion Collection 2. We were quite pleased to have it featured on BremSter's channel on 9 August 2022.

Estimated difficulty: 2.5-3/5

*Rules*

Normal 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 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}. Since all modular lines in this puzzle are on thermos, digits may not repeat along the modular lines.

Thermometers: Digits on thermometers must increase from bulb to tip, not necessarily consecutively. Each thermometer is also a modular line running from bulb to tip. Thermometers extending from the same bulb are distinct modular lines; that is, modular lines do not necessarily cross over bulbs from one thermometer to the next.

A mix of German whispers and modular lines that will make your eyes go fuzzy as you try to keep track of which is which along the rows.

Estimated difficulty: 2.5/5

*Rules*

Normal sudoku rules apply: every row, column, and box must contain a complete set of the digits 1-9. *XV*: Digits separate by a V sum to 5. Digits separated by an X sum to 10. Not all possible or Vs are given (no negative constraint). *German whispers*: The green flag stripes starting in rows 4, 6, and 8 of the flagpole in column 1 are German whispers lines. Adjacent digits along these lines must differ by at least 5. *Modular lines*: The teal flag stripes starting in rows 5, 7, and 9 of the flagpole in column 1 are modular lines. Each set of three adjacent digits along these lines must contain one digit from each of the residues classes mod 3; that is, one digit from {147}, one digit from {258}, and one digit from {369}. The flagpole is a separate modular line.

It's not the heat ...

This puzzle was first published to the July 2022 monthly puzzle prompt on the CTC Discord server for the weather and meteorology prompt.

Estimated difficulty: 1.5/5

*Rules*

Standard sudoku constraints: each row, column, and box must contain a complete set of the digits 1-9. Standard *thermometer constraint*: digits on thermometers must increase from bulb to tip.

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.

What better constraint for a Bastille Day puzzle than fortress cells? We sent this in to Cracking the Cryptic on a whim and were delighted to have it featured on 14 July 2022. It also appears in Indigestion Collection 2.

Estimated difficulty: 2.5/5

*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.

Standard thermometer constraint: digits on a thermometer must increase from bulb to tip.

Watch a solve of the puzzle by Mark Goodliffe on Cracking the Cryptic

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. It also appears in the Heartburn Collection.

Estimated difficulty: 4.5/5

*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*).

Isobars was set in response to the July 2022 monthly puzzle prompt on the CtC Discord server: puzzles related to weather and meteorology. Isobars are lines of constant or equal pressure on a weather map. It also appears in the GAS Collection.

Estimated difficulty: 1.5/5 (GAS-level)

*Rules*

Normal sudoku constraints: every row, column, and box must contain a complete set of the digits 1-9. *Kropki pairs*: cells separated by a white dot form a consecutive pair. Not all possible dots are given. *Isobars (blue lines)* have the same pressure along the entire line: either all the digits are low {1,2,3}, all the digits are middle {4, 5, 6} or all the digits are high {7, 8, 9}.

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: 3/5

*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: The digits on either side of a peach dot are in a k:1 ratio, where k is a whole number to be determined by the solver. Different kropki dots may have different values of k.

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.

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 also appears in the Heartburn Collection.

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 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 also appears in Indigestion Collection 2.

Estimated difficulty: 2/5

*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 may repeat on a line if allowed by other rules.

XV constraint: Digits separated by an X sum to 10. Digits separated by a V sum to 5. Not all possible X's or V's are necessarily shown.

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