Eureka
The Eureka notation system is a compact method to write Alternating Inference Chains.
Cells are mainly written in the rncn notation, but other methods like k9 can also be used.
Candidate digits are written as a prefix to the cell, with the digit number in parenthesis. This is the way to write candidate for digit 1 in the cell at row 5 and column 4.
(1)r5c4
Weak links are represented by a dash.
(1)r5c4-(1)r5c8
Strong links are represented by an equal sign.
(1)r5c8=(1)r9c8
There is no need to repeat the cell name when multiple candidates of that cell are used in the chain. A link between 2 candidates in a single cell is placed inside the parenthesis.
(1-4)r5c4=(4)r5c8
When groups of cells are used in the chain, they are named in the most efficient way.
- All cells belong to a single row
(1)r5c456
- All cells belong to a single column
(1)r45c4
- Unordered group, in a box
(1)r5c4|r6c45
When all candidates represent the same digit, this digit can be placed before the entire chain as a prefix.
(1): r5c4-r5c8=r9c8
When an embedded ALS is part of the chain, the digit linked to the previous node is isolated from the remaining digits with a strong link symbol. The remaining digits are placed in such an order that the digit linked to the next node is the last one.
(1)r5c4-(1=264)r5c789-(4)r4c8
When read from left to right, the chain must contain alternating strong and weak links. There can be no 2 adjacent dashes or equal signs, whether or not they are placed inside the parenthesis.
The result is placed after the chain, separated by a double arrow.
(1)r5c4-(1=4)r5c8-(4)r9c8=(4-1)r7c7=(1)r7c4-(1)r5c4 => r5c4<>1
