Kyudosudoku
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Variety Sudoku constraints

Each puzzle may have additional graphics in or around the Sudoku grid, which represent additional constraints that must be followed in order to arrive at the correct solution.

These are explained in-game with a tooltip (which you can turn on and off by toggling the tooltip button). For the curious, here is a complete list of them.

Odd/even | Anti-bishop | Anti-knight | Anti-king | No-consecutive | Maximum cell | Minimum cell | Find the 9 | Means | Consecutive neighbors | Double neighbors | Clockface | Inclusion | Battenburg | Killer cage | Renban cage | Thermometer | Arrow | Palindrome | Between line | German whisper | Snowball | Diagonal sum | Sandwich | Toroidal sandwich | Skyscraper | Skyscraper Sum | Battlefield | Binairo row/column | X-sum | Y-sum

Odd/even

The digit in this cell must be odd.

The digit in this cell must be even.

 8 1
✗ Invalid.
 3 6
✓ Valid.

Anti-bishop

The same digit can’t be on a diagonal (bishop’s move in chess) from this digit.

 3 3
✗ Invalid.
 6 3
✓ Valid.

Anti-knight

The same digit can’t be a knight’s move in chess away from this digit.

 2 2
✗ Invalid.
 7 2
✓ Valid.

Anti-king

The same digit can’t be a king’s move away (orthogonally or diagonally adjacent) from this digit.

 5 5
✗ Invalid.
 8 5
✓ Valid.

No-consecutive

A digit that’s 1 more or 1 less than this digit can’t be orthogonally adjacent to it.

 6 7
✗ Invalid:
6 and 7 are consecutive, so the 6 can’t be orthogonally adjacent to the 7.
 2 7
✓ Valid.

Maximum cell

This digit must be greater than the digits orthogonally adjacent to it.

 1 5 7 9 2
✗ Invalid:
9 is greater than 7.
 1 5 7 4 2
✓ Valid.

Minimum cell

This digit must be less than the digits orthogonally adjacent to it.

 9 5 3 1 8
✗ Invalid:
1 is greater than 3.
 9 5 3 6 8
✓ Valid.

Find the 9

The digit in this cell indicates how far in the indicated direction the 9 is.

 3 8
✗ Invalid:
The digit pointed to is not a 9.
 3 9
✓ Valid.

Means

Consider all three-cell lines centered on this cell. Exactly 1 of these must have the center cell be the arithmetic mean ((a+b)/2) of the flanking cells, and exactly 1 of them the geometric mean (√(ab)).

 1 7 4 5 3 1 2 8 7
✗ Invalid:
This example contains two arithmetic means (2-3-4 and 1-3-5) and no geometric means.
 1 7 4 5 3 2 2 8 9
✓ Valid.

Consecutive neighbors

The two marked cells must be consecutive (have a difference of 1).

 3 7
✗ Invalid:
3 and 7 are not consecutive numbers.
 3 4
✓ Valid.

Double neighbors

The two marked cells must have a ratio of 2 (one is double the other).

 2 6
✗ Invalid:
6 is not twice 2, and 2 is not twice 6.
 2 4
✓ Valid.

Clockface

The digits around the circular arrow must ascend in clockwise order.

The digits around the circular arrow must ascend in counterclockwise order.

 3 7 9 5 2 3 4 6
✗ Invalid.
 3 5 9 8 2 8 4 7
✓ Valid.
337

Inclusion

The four cells around the circle must contain the digits 3, 3 and 7 in some order.

 3 5 7 8 337
✗ Invalid:
Since the 3 is specified twice, it must occur at least twice.
 3 5 7 3 337
✓ Valid.

Battenburg

The four cells around the clue must form a 2×2 checkerboard of odd and even digits.

 3 1 4 8
✗ Invalid:
3 and 1 are both odd and next to each other.
 3 6 4 9
✓ Valid.
10

Killer cage

Digits within the cage must be different.

Digits within the cage must be different and must add up to 10.

 5 3 5 2 7 10
✗ Invalid:
In the first cage, the 5 repeats. In the second cage, 2 + 7 is not 10.
 5 3 6 2 8 10
✓ Valid.

Renban cage

Digits within the cage must be different and form a consecutive set.

 5 3 7 1 6 2
✗ Invalid:
Digits 1–3 and 5–7 occur. The 4 is skipped.
 5 3 7 4 6 2
✓ Valid.

Thermometer

Digits must increase from the bulb.

 9 7 8 2 4
✗ Invalid:
4 is less than 7.
 9 4 8 2 7
✓ Valid.

Arrow

The digits along the arrow must sum to the digit in the circle. (These digits need not necessarily be different.)

 1 1 3 8 2
✗ Invalid:
The digits add up to 7, but the circle does not contain a 7.
 1 1 3 7 2
✓ Valid.

Palindrome

The digits along the line must form a palindrome (same sequence of digits when read from either end).

 1 2 5 2
✗ Invalid:
The first and last digit are different.
 5 2 5 2
✓ Valid.

Between line

The digits along the line must be numerically between the digits at the ends.

 8 3 2 5 7
✗ Invalid:
The 2 is not between 3 and 8.
 8 2 3 5 7
✓ Valid.

German whisper

Adjacent digits along the line must have a difference of at least 5.

 7 3 2 7 8
✗ Invalid:
The first two digits (7 and 3) have a difference of only 4.
 7 1 2 7 8
✓ Valid.

Snowball

One of the regions must contain the same digits in the same places as the other, plus or minus a consistent addend. For example, if one region contains 1, 4, 7, the other might contain 3, 6, 9 in the same order. (The digits within one region need not necessarily be different. The addend can be zero.)

 1 4 7 3 5 8
✗ Invalid:
3 is 2 more than 1, but 5 and 8 are only 1 more than 4 and 7.
 1 4 7 3 6 9
✓ Valid.
8

Diagonal sum

The digits along the indicated diagonal must sum to the specified total. (The digits need not necessarily be different.)

 3 6 8
✗ Invalid.
 2 6 8
✓ Valid.
17 3 7

Sandwich

Within this row, the digits sandwiched between the 3 and the 7 must add up to 17. The 3 and 7 can occur in either order.

 4 1 5 3 9 8 6 7 2 17 3 7
✗ Invalid:
The digits between the 3 and 7 are 9+8+6 = 23.
4 1 5 3 9 8 7 6 2 17 3 7
✓ Valid.
3 7 17

Toroidal sandwich

Within this row, the digits after the 3 and before the 7, wrapping around the edges of the grid if necessary, must add up to 17.

 4 1 5 7 9 8 6 3 2 3 7 17
✗ Invalid:
The digits after the 3 and before the 7 are 2+4+1+5 = 12.
4 1 5 3 9 8 7 6 2 3 7 17
✓ Valid.
3

Skyscraper

Within this row, the digits represent skyscrapers, where taller ones obstruct the view of smaller ones behind them. 3 skyscrapers are visible from the clue.

 2 7 8 5 9 6 1 4 3 3
✗ Invalid:
The 8 obstructs the 5, and the 9 obstructs the rest of the row, leaving 4 skyscrapers visible (2, 7, 8, 9).
2 7 5 9 6 1 4 3 8 3
✓ Valid.
Σ 38

Skyscraper Sum

Within this row, the digits represent skyscrapers, where taller ones obstruct the view of smaller ones behind them. The heights of the skyscrapers visible from the clue sum up to 38.

 4 1 6 5 2 7 3 8 9 Σ 38
✗ Invalid:
The obstructed skyscrapers are 1, 5, 2, and 3. The rest sum up to 4+6+7+8+9 = 34.
3 5 6 4 7 2 8 9 1 Σ 38
✓ Valid.
20

Battlefield

The first and last number in the region represent the sizes of two armies, who march inward; the clue (20) specifies the sum of the digits that are either sandwiched between the armies or within the armies’ overlap.

 5 1 4 6 7 3 9 2 8 20
✗ Invalid:
The armies (sizes 5 and 8) overlap at the 1, 4, 6 and 7, which adds up to 18.
2 1 8 5 7 3 9 6 4 20
✓ Valid.

Binairo row/column

In this row, no three adjacent digits can be all odd or all even.

 1 5 4 6 7 3 9 8 2
✗ Invalid:
7/3/9 are three odd digits next to one another.
1 5 4 3 7 6 8 9 2
✓ Valid.
XΣ 19

X-sum

The sum of the first X digits in this row must add up to 19, where X is the first digit in the row.

 5 7 6 2 1 9 8 4 3 XΣ 19
✗ Invalid:
The first 5 digits are summed, giving 5+7+6+2+1 = 21.
4 7 6 2 1 9 8 5 3 XΣ 19
✓ Valid.
YΣ 19

Y-sum

The sum of the first Y digits in this row must add up to 19, where Y is the Xth digit in the row and X is the first.

 7 4 2 6 1 9 8 5 3 YΣ 19
✗ Invalid:
The first digit is 7. The 7th digit is 8. Therefore, we sum the first 8 digits, which gives 7+4+2+6+1+9+8+5 = 42.
2 4 7 6 1 9 8 5 3 YΣ 19
✓ Valid.