Up till now, our description of xy-chain is of a repetitive type and would only allow us to eliminate one candidate from one cell as posted here.

However, if a non-repetitive xy-chain can be identified, it would allow us to possibly eliminate candidates from every unit where each edge of the chain lies. The name 'non-repetitive' implies that none of the consecutive edges on the chain have the same label.

Let me demonstrate via 2 examples:

The chain is: starting from r1c2, [89]-[92]-[21]-[13]-[35]-[58]. Due to the existence of this non-repetitive xy-chain, 3 and 8 can be eliminated from r3c7 and r1c3 respectively.

The chain is: starting from r1c7, [29]-[91]-[13]-[37]-[74]-[47]-[74]-[42]. Due to the existence of this non-repetitive xy-chain, 7, 24 and 7 can be eliminated from r4c1, r9c7 and r4c9 respectively.

These chains can be identified by pure inspection of bevalue cells as follows:

1) Choose one cell to start with and mark down the first candidate.

2) Propogate through the grid with cells that lie on the same unit.

3) Match the last candidate of the cell with the first candidate of the next cell.

4) Repeat the process until a cell (last cell) is found lying in the same unit with the starting cell.

5) If the last candidate of the last cell matches the first candidate of the starting cell, then congratulations, you have found a non-repetitive xy-chain.