Remote pairs: alternate the same pair along a chain
Remote pairs form a chain of bivalue cells that all contain the same two digits. Consecutive cells must see each other.
Key idea
An even number of cells means an odd number of links, so the endpoints take opposite values. A cell seeing both endpoints can contain neither digit.
See the move, step by step
Follow four 5/7 cells from R1C1 to R7C6. The endpoints share no row, column or box. This constructed candidate state includes earlier deductions.
Step 1 of 4
Find repeated bivalue cells
Locate cells that contain exactly the same pair, 5 and 7, and can be connected through shared units.
Step 2 of 4
Alternate the chain
R1C1 to R1C5 uses row 1; R1C5 to R2C6 uses box 2; R2C6 to R7C6 uses column 6. Four cells and three links give opposite endpoint values.
Step 3 of 4
Check cells seeing both endpoints
R7C1 sees R1C1 through column 1 and R7C6 through row 7. One endpoint is 5 and the other is 7 in either chain state, so remove both digits from R7C1.
Step 4 of 4
Remove both pair digits
R7C1 retains 3 and 9. All four chain cells keep 5 and 7; the chain does not determine which alternating state is true.
Try it on today's puzzle
Trace both possibilities: 5–7–5–7 or 7–5–7–5. Four cells have three links and opposite endpoints; five cells have four links and equal endpoints, which does not justify this elimination. Every adjacent pair must share a unit and contain exactly the same two candidates. The target must see both endpoints.
Play today