Logic Masters Deutschland e.V.

Hello.

I am very excited to introduce this new constraint especially after seeing how much Simon loved it when it appeared on Cracking the Cryptic

Note: This puzzle has only one additional rule, and it’s simpler than it might first appear. Take a few seconds to read it carefully and a couple of minutes to get used to it. The example should make everything clear.

Normal sudoku rules apply.

BitClock: Each BitClock consists of an arrow cell at the centre of the clock and its four orthogonal neighbours. The digit in the arrow cell encodes the parity (odd or even) of those four neighbours.

Even digits represent bits that are ON (E), and odd digits represent bits that are OFF (O). The corresponding 4-bit code for each digit (read from left to right) determines the parities of the four adjacent cells.

The arrow indicates the starting bit of the sequence, which continues clockwise around the BitClock.

Example:
If a 3 is placed in a BitClock cell, its code is OOEE.
Starting from the direction of the arrow and reading clockwise, the four orthogonal neighbours must be Odd, Odd, Even, Even.

Digit Codes:


1 → OOOE


2 → OOEO


3 → OOEE


4 → OEOO


5 → OEOE


6 → OEEO


7 → OEEE


8 → EOOO


9 → EOOE

Have fun.

Understanding the Binary Behind BitClocks

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.

Why this matters for solving

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.

Spoiler

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.