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Tue, 26 May 2020

# Solving Hanjie Puzzles

Hanjie Puzzles are rarely seen in publication, yet they tend to become something of an addiction for those who are bitten by the hanjie bug.

Hanjie is a type of logic puzzle, and it consists of a rectangular grid with various numbers around the outside of the grid, typically at the start of each row and at the beginning of each column.

These numbers outline how many cells within each row or column - called a region - are to be filled in. The finished puzzle will consist of every cell within a row or column being fully determined as either empty (marked with a dot) or filled in (usually coloured in in black though any colour would do with a black and white puzzle).

At the end of the hanjie puzzle, there will be a simple image revealed by the combination of the filled cells in each row and column.

With hanjie there is one other thing to know: the number outside a region may be split into several parts: eg it might be 2,8. This means that there are two filled sets of cells in that region, with at least one blank/empty cell between them. Were that not the case, then the clue would simply have been 10.

Therefore if the region were of length 11, then you could place this straight away, as the minimum expanse necessary for a 2,8 clue is 11 cells (2 + 1 + 8) and therefore this can be placed straightaway in the grid.

When solving hanjie puzzles, the first place to look is for any 0 regions - those where every cell is to be marked as blank.

Next up, look for regions where a high number of cells are to be coloured in. In this instance you can usually place at least some cells straight away - look for instances where more than half of the cells in a region are to be filled to definitely apply this rule.

As a simple example, if the puzzle is a mini 5 x 5 puzzle, and the clue for the first row is 3, then you can fill in the central cell of the row. Why is this? Because that square must be filled in with every combination, as the options are (with 'F' being 'filled' and 'B' being 'blank'):

FFFBB
BFFFB
BBFFF

Reading down the columns, you can see that in each case, the third cell is filled, and therefore it can be marked in.

Look for opportunities to apply this rule at the start of solving a hanjie puzzle to get any quick and easy placements in.

Many hanjie puzzles require you to go through each row and column repeatedly looking for cells that must be either filled in or empty, and then going around again and again each time whittling down the options and placing more cells.

However, some puzzles that are harder may require you to cross-reference between regions - there is a debate as to whether this is a 'fair' solving method or not, with some people being happy with it, but the majority of solvers prefer the more straightforward method of solving where you never need to cross-reference: this is more than capable of making tough puzzles, particularly with large grid sizes where it could be the case that out of thousands of combinations there may be one cell that always happens to be in the same place: this can be very tricky to spot!

With a good hanjie puzzle there is only one solution that can be reached through logic alone.

Finally, there is a variant of hanjie called colour hanjie - here cells may be filled in with more than one colour, and this is indicated by clue numbers of different colours around the edge of the grid - hopefully that puzzle will be the subject of a future world of puzzles blog entry!

If you like hanjie puzzles, then why not print out a copy of Hanjie Magazine, which contains 50 hanjie puzzles in a PDF magazine for you to print off and enjoy.
Date written: 10 Feb 2012

Category: hanjie | Keywords: hanjie

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If you've never solved a sandwich sudoku, then a 6x6 puzzle is a good place to start. You can have a go at solving the puzzle featured in the video here: 6x6 Sandwich Sudoku Puzzle Online

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