Slitherlink: try both ways

When the counting rules stop, pick a side and suppose it went one way. If the rules break, it goes the other way.

The 0s and the corner 3s are done, and nothing else moves. Look at the 2 in the top right corner.

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How it works

Sometimes no number, dot or pattern moves anything. Then the next step is a short proof by contradiction.

Pick a side next to something you know. Suppose it is ×, and follow the counting rules from there. If a dot or a number breaks, the side must be a line. Then try the other way too.

Choosing a side to try

Try sides next to numbers or next to a dot that already has a line or a cross. The rules start moving at once there, so a break shows up in a few steps.

If neither case breaks, look at what both cases drew. A mark that appears either way is certain too.

Worth memorizing

Suppose one way, follow the rules.
If a rule breaks, the other way is true.
If both ways draw the same mark, that mark is certain.

Practice

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Question 1

Supposing the top side of the corner 2 is × breaks a rule. What is that side?

Where you’ll use this

Proof by contradictionThe logic behind it Slitherlink: dots, counts and one loopThe rules you follow in each case Play SlitherlinkThursday to Sunday need it

Play today’s SlitherlinkPut this lesson to work Next: Star Battle: regions that own rowsIf a region fits inside one row, that row’s two stars are the region’s. Dot the rest of the row. Two regions inside two rows work the same way.