Nice loops: close an alternating inference chain

A nice loop is a closed chain of candidate nodes joined by strong and weak links. The link sequence must remain logically continuous around the loop.

Key idea

When a discontinuity or outside peer conflicts with every valid loop state, its candidate can be eliminated.

See the move, step by step

Trace a four-node loop for candidate 7 across rows 1 and 3.

Step 1 of 4

Choose a candidate network

Filter for candidate 7 and locate conjugate pairs that can be connected through shared units.

Rows containing the loop

Step 2 of 4

Alternate strong and weak links

The four corner candidates form a closed loop: strong across each row and weak up each column.

Loop unitsAlternating candidate loop

Step 3 of 4

Use the loop's consequence

R5C1 sees both loop states along column 1, so candidate 7 cannot remain there.

Nice loopCandidate to remove

Step 4 of 4

Keep the loop, remove the outsider

The loop itself stays unresolved while R5C1 loses candidate 7.

Nice loopUpdated target

Try it on today's puzzle

Draw every link explicitly. A strong link means at least one endpoint is true; a weak link means both cannot be true. Do not alternate by appearance alone.

Play today