GridWits
Hard tier Technique 7 of 8 Used by Smart Hint

Cut-Bridge Parity

This is the only possible connection across a cut: it must be positive, and the clue sum on either side determines whether it is single or double.

How it works

  1. 1Ignore the highlighted connection for a moment: the four highlighted islands have no other possible route to the islands on the right, so this edge is a cut bridge of the remaining network.
  2. 2The finished bridge network must be connected, which means the cut bridge cannot carry zero.
  3. 3The highlighted clues sum to 10. Bridges wholly inside the group contribute twice to that sum, so the one boundary edge must contribute an even number.
  4. 4A positive Hashi edge is either 1 or 2; the only positive even choice is 2, so draw the double bridge.
2 2 2 4 4 2 2
  • Bridge to add
  • Islands that establish the pattern
Next in the ladder Contradiction →

Suppose a connection carried its lowest (or highest) possible count and follow the consequences — if an island overflows, bridges cross, or a finished group gets sealed off, that count is ruled out.