Plankway

Try and see: following an assumption to a contradiction

Sometimes none of the direct techniques gives a new bridge. Then there is one more step: take a choice, assume it is true for a moment, and follow what the simple techniques say next. If that leads to something impossible, the assumption was wrong, and you have learned something certain.

This is not guessing

Guessing means placing a bridge and hoping. Trying and seeing means proving: you only keep what you have shown must be true. The assumption is thrown away; the conclusion stays. That is why Plankway can promise that every puzzle is solvable without guessing, even on Sundays.

A small example

Suppose the 2 in A1 and the 2 in D1 were connected with a double bridge.

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Assumption: a double bridge between the two 2s (dashed).

Both 2s would be full. Then the 1 in A4 and the 1 in D4 could only connect to each other. That gives two separate networks, which breaks the last rule.

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Following the assumption: the two 1s end up in their own group. Impossible.

So the double bridge is wrong: there is at most one bridge between the two 2s, and the rest follows.

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The solution: single bridges all around.

In this small case avoid isolation sees it directly. In real weekend puzzles the chain is longer, a few steps of counting before the contradiction appears, but the way of thinking is exactly the same.

How to do it well

  • Pick a connection with only two options, for example "single or double" or "bridge or no bridge". Then one of the two must be true.
  • Follow only the simple techniques: full islands, every bridge counts, crossings and limits. Keep the chain short.
  • Look for these contradictions: an island with too many bridges, an island that cannot get enough, or a group that is closed off.
  • If no contradiction appears, you have learned nothing, and that is fine. Try the other option, or another connection.

The Plankway solver does exactly this, and gives it the highest weight, 6. A puzzle that needs it is rated "expert"; you will find those in the archive mostly on Saturdays and Sundays.

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