5 Houses


Step 1.   The setup.

I used Microsoft Works spreadsheet to set up a matrix of houses.

I saved an image of this to serve as sort of a game board with which to place pieces.

Then I filled in what I could of the clues onto the matrix.   These were clues 1, 2 and 12.

Starting Matrix

I combined clues and added them as new clues after the 15 original clues

Clues list

I made a piece with transparent background for each of the clues not accounted for by direct placement on the matrix.

Each piece is numbered after the clue that it corresponds to.   You will have to zoom in on this to match the matrix size.

Pieces

After you verify that the pieces correspond to the clues you can close the clue list.

Then I started a text file with which to keep track of the sequences of piece placement.

I placed the larger pieces first as they have less possible positions to occupy but went in order of the letters for alternative pieces.

I placed the remaining in order of those with least possible positions first.

When I reached a piece that wouldn't fit I backtracked methodically to the last branch where there was an alternative.


Step 2.   The sequence.

piece position comment
18a 2 first of three possible positions
16 5 only possible position
    17a wont fit
17b 4 only possible position
    3 wont fit
    Since we have to have one 17 and piece 16 we must start all over with 18a in the next possible position.
18a 4 second of three possible positions
    16 won't fit
18a 5 third of three possible positions
16 5 only possible position
17a 3 only possible position
    3 wont fit
17b 2 first of two possible positions
3 3 only possible position
4 4 only possible position
5 2 only possible position
    15 wont fit
17b 4 second of two possible positions
    3 wont fit
    Since 18a at 5 is the last possible position for this piece we know that 18a is an impossible case so we start all over with 18b
18b 3 first of two possible positions
16 5 only possible position
17a 3 only possible position
    3 wont fit
17b 2 first of two possible positions
3 3 only possible position
15 5 only possible position
5 2 only possible position
6 4 only possible position
    9 wont fit
17b 4 second of two possible positions
    3 wont fit
18b 4 second of two possible positions
16 5 only possible position
    17a wont fit
17b 2 only possible position
3 3 only possible position
9 5 only possible position
    15 wont fit
    Since this was the last possible position for 18b we know that 18b is an impossible case. We start all over with 18c.
18c 2 first of three possible positions
16 5 only possible position
17a 3 only possible position
    3 wont fit
17b 2 first of two possible positions
3 3 only possible position
15 5 only possible position
5 2 only possible position
6 4 only possible position
9 3 only possible position
4 5 only possible position
 

Since there is only one place for the fish we know that it is the German who keeps the fish.

It appears we have a solution but first we need to check it against all the clues.

What if someone else hands you their solution and since it differs from yours you proudly tell them its wrong?
  Well wouldn't you be embarrassed to find out that their solution met all the criteria and was therefore also correct?   We must continue this process for the remaining position for piece 17b, remaining two positions for piece 18c and all possible positions for piece 18d to find all possible solutions or determine that our solution is unique.

The remainder of the sequence follows without diagrams.

piece position comment
17b 4 second of two possible positions
    3 wont fit
    So no more solutions involving 18c. Last 18 to try is 18d
18d 4 first of two possible positions
    16 cant fit
18d 5 second of two possible positions
16 5 only possible position
17a 3 only possible position
    3 wont fit
17b 2 first of two possible positions
3 3 only possible position
5 2 only possible position
    15 wont fit
17b 4 second of two possible positions
    3 wont fit

We reached the end of all the possibilities without finding another solution which means that the solution we found is indeed unique!

If you want the multi-layered Paint Shop Pro files that I made to solve this e-mail me at AjiSabaki@hotmail.com