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Hashi puzzle solution
This is an example of a completed Hashi (also known as Bridges) puzzle. The grid is made up of a series of islands (the circles) connected by lines, or 'bridges'. Each clue tells you how many bridges are connected to that islands.
A couple of additional rules:
  1. All the islands and bridges must be one connected whole.
  2. There can't be more than 2 bridges between two islands.
  3. Connecting bridges can't cross each other.
  4. Bridges can only be horizontal or vertical, not diagonally.
Hashi puzzle
I've highlighted 3 clues here that we can use to start this puzzle. Firstly, look at the highlighted island with the '1' clue. There are two islands this island can be connected, either the '1' to it's right, ro the '2' under it. If it was connected to the other '1', then you wouldn't be able to add any more bridges to either of those islands, and that would violate rule 1 from above. So the highlighted '1' island must be connected to the '2' under it.
Now look at the highlighted '7' island. This island has other islands in all four directions, to give a maximum of 8 bridges out from this island (2 for each direction). Three of those directions will have 2 bridges, and the other will have 1 bridge. Each direction will have a minimum of 1 bridge, so we can draw 1 bridge in each direction.
Next, look at the highlighted '5' island. We can apply the same logic as the previous island, but it only has 3 neighbours, to give a maximum of 6 bridges out from this island. We can apply the same logic to decide there must be a minimum of 1 bridge out in each direction.
Hashi puzzle
Placing those bridges gives us this grid. Notice that each island will turn to green when all of the bridges for that island had been put in place.
We can apply these two techniques to a lot of the other islands in this puzzle. Also, look at the highlighted '4' in the top right, this island has 4 connecting bridges, so there must 2 bridges from each direction for this island.
Hashi puzzle
We are now at this point, and we can use the same set of techniques to fill in more bridges. The '2' clue on the left hand side already has one bridge, but there is only one option for the other bridge, i.e. to the '4' to it's right, so we can add a bridge here.
We have a set of '4' clues in a line, let's start with the top clue. This clue can only form bridges with two other clues, the '2' to it's right and the other 4 under it, so we can add 2 bridges to the right and 2 downwards.
The middle '4' clue has a maximum of 5 bridges it can form, since we can only form a maximum of 1 bridge downwards, there must be at least one bridge to the right
The bottom '4' clue already has one bridge, with another four possible bridges. We can conclude that we must have at least one bridge upwards and at least one to the right.
Hashi puzzle
There aren't that many bridges we can insert in to the puzzle at this stage, so you have to look quite hard. The highlighted '1' clue only has one island it can connect to now - the '2' to it's left has it's full allocation of two bridges, so this island's bridge must be downwards to the '2'.
The highlighted '2' clue has two possible direction it can form bridges, but to it's right is a '1' clue, so at least one bridge must be downwards.
We are now starting to see some partitioning in the puzzle; bridges are being put in place that will block islands from each other.
Hashi puzzle
Look at the '5' clue, this clue only has three other islands it can form bridges with now - it has been blocked off to the '1' to it's left. There must be at least one bridge in each of the three directions left.
This has consequences for the highlighted '2'. It has been cut off from the '1' to it's right, so it's other bridge must be downwards to the '3'.
The highlighted '3' clue has also been cut off from the '1' to it's right, so it must have a bridge downwards.
The highlighted '1' clue has also been cut off from all other clues apart from the '3' below it.
Hashi puzzle
You now have all the skills you need to solve a Hashi puzzle. I have highlighted another five clues that you can now draw all the lines for. (Hint: Start with the smaller numbers).
This puzzle is the daily puzzle from Thursday 7th March 2019, feel free to continue solving this puzzle if you wish!

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