Spirals: a 7x7x7 sudoku pack

Well... indeed I initially intended to create 7 puzzles, but in the end there were 9. Stubborn as I am, I'm sticking to the 7x7x7 title.

You see, the idea was to create an interesting 7x7 irregular sudoku grid, and then select seven variants to create seven different puzzles with this grid, each with a single given digit. Without thinking, I started with a 147 indexing puzzle, but one given digit in such a puzzle is never going to collapse it into a unique solution. It was too good though to not publish. So there's the first bonus.

The second variant I tried that I should have thought a bit more deeply about was one with odd and even cells. To make that more interesting I added white kropki dots, and got some unusual deductions out of that. But that puzzle also didn't fit the premise of a single variant per puzzle with one given digit. With some modifications I could still use it as an introductory puzzle from which to obtain the given digits in the 7 core puzzles. And there's the second bonus.

Without further ado, here is the intro puzzle:

Spirals, puzzle O

For each of the nine puzzles, normal irregular 7x7 sudoku rules apply: place the digits 1 to 7 exactly once in each row, column, and region indicated by thick borders in the grid.

Furthermore:

• Odd/Even:
• Cells with an opaque grey circle must contain an odd digit.
• Cells with an opaque grey square must contain an even digit.
• Kropki pairs:
• Wherever a white dot appears on a border between two cells, those two cells must contain digits that are different by exactly 1 (such as 4 and 5).
• Wherever a black dot appears on a border between two cells, those two cells must contain digits that are in a ratio of 1 to 2 (such as 6 and 3).
• The converse is not true, if a white or black dot could appear between two neighboring cells, it is not necessarily given in the grid.

The colors indicate where the seven given digits are in each of the seven subsequent puzzles. They are not necessary to solve the puzzle.

You can play puzzle O online in the CTC app.

Spirals, puzzle I

• The digit in the yellow cell (row 4, column 2) must be the same as the digit at the same location in puzzle O.
• XV pairs:
• Wherever a 'V' appears on a border between two cells, those two cells must contain digits that add up to 5 (such as 4 and 1).
• Wherever an 'X' appears on a border between two cells, those two cells must contain digits that add up to 10 (such as 3 and 7).
• The converse is not true, if a 'V' or 'X' could appear between two neighboring cells, it is not necessarily given in the grid.

You can play puzzle I online in the CTC app.

Spirals, puzzle II

• The digit in the grey cell (row 1, column 3) must be the same as the digit at the same location in puzzle O.
• Arrows: Digits along an arrow in the grid must sum to the digit in its circle (such as 2+2 = 4).

You can play puzzle II online in the CTC app.

Spirals, puzzle III

• The digit in the blue cell (row 7, column 3) must be the same as the digit at the same location in puzzle O.
• Diagonal: Digits must not repeat on the indicated main diagonal in the grid, running from the top left to the bottom right corner.
• Thermometers: Grey paths indicate thermometers. Digits in thermometers must strictly increase moving away from the bulb (circle).

You can play puzzle III online in the CTC app.

Spirals, puzzle IV

• The digit in the dark blue cell (row 1, column 5) must be the same as the digit at the same location in puzzle O.
• Killer cages: An area surrounded by a dashed line is a 'killer cage'. Digits in a cage cannot repeat and sum to the number in the upper left corner.

You can play puzzle IV online in the CTC app.

Spirals, puzzle V

• The digit in the pink cell (row 5, column 6) must be the same as the digit at the same location in puzzle O.
• Between lines: Digits on a line connecting two circles must be strictly between the digits in those circles. (I.e. the digit in one circle is greater than all digits on the line, while the digit in the other circle is smaller than all digits on the line.)

You can play puzzle V online in the CTC app.

Spirals, puzzle VI

• The digit in the dark green cell (row 3, column 3) must be the same as the digit at the same location in puzzle O.
• Quadruples: Digits in circles within the grid must appear at least once somewhere in the four cells adjacent to the circle.

You can play puzzle VI online in the CTC app.

Spirals, puzzle VII

• The digit in the red cell (row 4, column 4) must be the same as the digit at the same location in puzzle O.
• Kropki pairs:
• Wherever a white dot appears on a border between two cells, those two cells must contain digits that are different by exactly 1 (such as 4 and 5).
• Wherever a black dot appears on a border between two cells, those two cells must contain digits that are in a ratio of 1 to 2 (such as 6 and 3).
• The converse is not true, if a white or black dot could appear between two neighboring cells, it is not necessarily given in the grid.

You can play puzzle VII online in the CTC app.

Spirals, bonus puzzle IIVVII

• 147 indexing: Digits in column 1 indicate the column in which the digit 1 appears in that row (e.g. if r3c1 is a 6, r3c6 is a 1). The same is true of column 4 and the digit 4, and column 7 and the digit 7.

You can play bonus puzzle IIVVII online in the CTC app.

All puzzles published on this blog are licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.