Logic Masters Deutschland e.V.

Hello!

I’m thrilled to introduce a new puzzle constraint I’ve named Bitclock.
My very first puzzle using Bitclocks was featured on Cracking the Cryptic.
If you enjoy it, there are several more on my page, where I’ve combined Bitclocks with other interesting constraint types.

Click image to play in SudokuPad

Normal sudoku rules apply.

BitClocks:

Each BitClock consists of:

-An arrow cell, and

-The four orthogonally adjacent cells around it.

The digit in the arrow cell encodes the parity (Odd/Even) of those four neighbouring cells.

Each digit 1–9 corresponds to a specific 4-bit parity code. (see table below)

The arrow indicates the first neighbour, and the code is read clockwise around the four adjacent cells.

Example:

If an arrow cell contains 3, its code is OOEE.

Starting from the direction the arrow points and moving clockwise, the adjacent cells must be Odd, Odd, Even, Even. (read from left to right)

Digit Codes:


1 → OOOE
            Even digit = ON (E)

2 → OOEO
            Odd digit = OFF (O)

3 → OOEE


4 → OEOO


5 → OEOE


6 → OEEO


7 → OEEE


8 → EOOO


9 → EOOE

Have fun.

Optional: The rest of this explanation is here for reference. You are encouraged to try the puzzle and discover the logic on your own before reading further.

Binary codes are sequences of bits where each bit has twice the value of the previous one.
A typical list of binary place values is:

… 32, 16, 8, 4, 2, 1

Binary is usually written with the largest value on the left and the least significant bit (LSB) on the right. This mirrors normal reading order and makes addition straightforward: you simply add the values of all the bits that are ON.

Since BitClocks only need four bits, we use the four values:

8, 4, 2, 1
(from left to right)

Examples

The digit 4 is written in binary as 0100
Only the 4-bit is ON; the 8-, 2-, and 1-bits are OFF.

The digit 5 is 0101
The 4-bit and the 1-bit are ON → 4 + 1 = 5.

In binary, the characters 0 and 1 do not literally mean “zero” and “one”; they simply mark whether a bit is OFF or ON.
Because BitClocks care about parity, we translate them like this:

• 0 → O → Odd (OFF)
• 1 → E → Even (ON)

So binary can be rewritten using O and E without losing any information.

Part of the enjoyment of BitClocks is discovering how these binary patterns interact, but the constraint can feel unusual at first. Here are a few conceptual hints to help you build intuition, without spoilers:

1. Think of the switches as ON/OFF controls
   Which switches are ON determine the value of the central digit.
   Cells that are switched ON must have an even digit, cells that are switched OFF must have an odd digit.
2. BitClocks mimic familiar constraints
   Because the bits add up to form the digit, some of the resulting logic works similarly to arrow sudoku.
   Because bits encode parity, some logic resembles white kropki dots, but without requiring digits to be consecutive.
   BitClocks combine these behaviours in a compact and surprisingly rich way.

3. High bits put pressure on the lower bits
   If the 8-bit is ON, the remaining three bits can only sum up to at most 1.
   This restricts the digit heavily (only 8 or 9 are possible).
   Conversely, if a 2-bit or 4-bit is ON, the 8-bit may be forced OFF.
4. The LSB (1-bit) is often the “tiebreaker”
   Because the 1-bit determines the parity of the central digit, this is often where to look when searching for relationships between odd and even.