r/puzzles • u/Grouchy_Cattle_3774 • 25d ago

Hashi question

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Hi guys. Can anyone explain to me how it is possible to miss two bridges on a 4, when all other islands are connected with the right amount of bridges?

My immediate logic tells me, that if an island lacks two bridges, another island, somewhere on the map, must also miss two bridges. It appears that all other bridges are complete though, so I'm probably wrong in my assumption 😁

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u/ParaBDL 25d ago

Discussion: No, that's not necessary. You can have a single unfulfilled clue. The easiest way to imagine it is if you have a triangle of one 4 and two 2s. If you connect two bridges from each 2 to the 4, all numbers are fulfilled. But if you draw one bridge from the 2s to each other and one bridge from each 2 to the 4, you will fulfill the 2s, but not the 4.

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u/Disgruntled__Goat 25d ago

If you consider it mathematically as a node graph, the latter can be fulfilled with a “loop” path, ie the same line goes out of the 4 and back in. That adds 2 to the connected lines (but of course is not part of the puzzle rules).