Build Bridges!

Logic Level 2

Below is a puzzle called Hashiwokakero , also known as Bridges :

The goal is to connect all of the islands by drawing a series of bridges between the islands. The bridges must follow certain criteria:

  • They must begin and end at distinct islands, traveling a straight line in between.
  • They must not cross any other bridges or islands.
  • They may only run orthogonally (i.e. they may not run diagonally).
  • At most two bridges connect a pair of islands.
  • The number of bridges connected to each island must match the number on that island.
  • The bridges must connect the islands into a single connected group.

How many bridges are connected to the unknown island (with a question mark on it)?


The answer is 2.

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Brack Harmon by Brack harmon , 18, USA

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3 solutions

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Stephen Mellor
May 10, 2018

Consider the island circled red. As the bridges must be parallel to the grid lines, it can only connect with the island circled blue. After this bridge, the only bridge that the blue island can make (as it needs 2) is with the island circled orange.

This cuts off the links from the unknown island meaning it can only be connected to the island circled green. As at most two bridges connect a pair of islands, we know this number is 0,1 or 2. However, it cannot be 0 as the green island wouldn't be able to get 5 bridges due to the same constraint of a maximum of 2 and the green island can only connect to 2 other islands.The total sum of the numbers must be even as each bridge adds 2 to the sum. Adding all up, we see that the current total is already even so the mystery island is also even. This eliminates the option of 1, leaving the answer as 2 \boxed{2}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Is there any provision for pictorial answers. It would have been quite better if we could see the bridges drawn on the graph.

Arghyadip Ojha - 3 years ago

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I did think about it, but I just left it such that the diagram is used to confirm which nodes I'm talking about

Stephen Mellor - 3 years ago
Brack Harmon
May 9, 2018

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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