Arrow maze

This page is about an arrow maze that I created either on August 26, 1980, or, more likely, on October 19, 1976.

First version

I started with a normal maze drawn on sheet with 5mm squares, my favourite drawing paper of that time. Then I drawed the arrows with pencil. Below a scan of this sheet.

What follows below, are the arrows as I think they are recorded on the first sheet.

Possible errors in this maze are:

2^nd row, 24^th column: arrow down and arrow right.
3^rd row, 25^th column: needless arrow.
7^th row, 39^th column: cannot be reached.
10^th row, 7^th and 8^th column: arrows point to each other.
12^th row, 23^rd column: arrow down.
12^th row, 24^th column: arrow left.
12^th row, 35^th column: needless arrow.
14^th row, 23^th column: arrow left.
18^th row, 23^th column: cannot be reached.
24^rd row, 14^th and 15^th column: arrows point to each other.

Second version

The second version was drawn on a white sheet. I layed this on top of the first sheet, and I copied the arrows from the first sheet. I marked the shortest route with red. And then I made some modifications. The scan of the sheet is given below.

What follows below, are the arrows as I think they are recorded on the second sheet.

Possible errors in this maze are:

3^rd row, 25^th column: needless arrow (like first).
37^th row, 32^nd column: arrow left missing.
38^th row, 15^th column: needless arrow.
41^st row, 34^th column: needless arrow.
42^nd row, 9^th column: needless arrow.
48^th row, 32^ndh column: needless arrow.
53^rd row, 22^nd column: needless arrow.
54^th row, 18^th column: cannot be reached.
54^th row, 37^th column: needless arrow.

It seems that a number of these errors were introduced because of copying mistakes from the first to the second version, where accidently some junctions were removed. For example, that the error on the 54^th row and 18^th column cannot be reached, is due to the fact that in 29^th column only has an arrow to the left, while in the first version it also contains an error to the right.

Corrected version

Because of all the (possible) errors that I noticed in the above versions, I decided (on April 21, 2006) to develop a program to verify these versions and to arrive at an error free version. I remember that one of my design objectives was that there should be no alternative paths from the start to the end such that the only correct solution would be complete overlapping with it. The following correction, I made before I developed the program:

37^th row, 32^nd column: changed this into a left and up arrow.

During the developed of the C++ program, I made a number of corrections. The first correction, where related to the fact that there was actually a shorter solution than the solution that I had intented. These are:

9^th row, 19^th column: added left arrow.
23^rd row, 8^th column: removed the down arrow.
55^th row, 14^th column: removed the left arrow.
57^th row, 14^th column: removed the left and up arrow.

To remove some alternative paths, I made the following correction:

7^th row, 25^th column: removed down arrow.
10^th row, 26^th column: removed the up arrow.

Futhermore, I made the following correction:

7^th row, 38^th column: added a right arrow to the left and up arrow, making some arrows reachable.

Undoing some changes made from the first to the second model, which possibly introduced some errors, such as needless arrows:

2^nd row, 19^th column: added a down arrow
20^th row, 11^th column: added left and up arrow
23^rd row, 16^th column: added up and right arrow
23^rd row, 19^th column: added down and left arrow
30^th row, 4^th column: added left and up arrow, making arrow in 27^th row reachable
32^nd row, 25^th column: added a down arrow, making arrow in arrow in 34^th row reachable
33^rd row, 31^st column: added left and up arrow, making arrow in 31^st row reachable
39^th row, 9^th column: added down and left arrow, making arrow in 42^nd row reachable
39^th row, 12^th column: added a right arrow
40^th row, 11^th column: added a down arrow
40^th row, 13^th column: added a right arrow
40^th row, 15^th column: added up and down arrow
48^th row, 33^rd column: added a left arrow, making arrow in 32^nd column reachable
49^th row, 7^th column: added a up arrow making arrow in 45^th column reachable
49^th row, 30^th column: added a down arrow, making arrow below reachable
51^st row, 7^th column: added a right arrow, making arrow in 10^th column reachable
51^st row, 32^nd column: added left and up arrow
52^nd row, 20^th column: added a up arrow
54^th row, 13^th column: added a up arrow
54^th row, 15^th column: added a up arrow
54^th row, 17^th column: added a right arrow, making arrow on the right reachable
54^th row, 29^th column: added a right arrow
55^th row, 10^th column: added right and down arrow, making arrow below reachable

This finally resulted in the following version:

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