# The Labyrinths with 3 Pseudo Double-barriers, 4 Arms, and 5 Circuits

In my last post I have shown, that there exist 64 labyrinths with 3 real and / or pseudo double-barriers, 4 arms, and 5 circuits (see: related posts, below). But, how many of these do have exclusively pseudo double-barriers?

This question could actually be answered with the material from the last post. In order to show this, I once again make use of the tree diagram (fig. 1). This shows the combinations that can be obtained based on labyrinth D. There we can see, that the uppermost combination results in a pattern made-up exclusively of real double-barriers (that is, labyrinth D). This is the only one of the eight patterns using only real double-barriers. Similarly, the lowermost combination results in the only pattern made-up exclusively of pseudo double-barriers. I will term this D’. The six combinations in between all result in patterns with mixed combinations of real and pseudo double-barriers.

Figure 1. Combinations with Real, Pseudo, and Mixed Double-barriers

Now, if we proceed the same way as in fig. 1 for all labyrinths A – H, we always will obtain a lowermost combination made-up exclusively of pseudo double-barriers. These patterns and the corresponding labyrinths are shown in fig. 2. I have termed them A’ – H’. Labyrinths with the same uppercase letter belong to the same tree diagram.

Figure 2. The 8 Labyrinths with 3 Pseudo Double-barriers, 4 Arms, and 5 Circuits

Thus, we can conclude, that among the 64 labyrinths there are

• 8 labyrinths with only real double-barriers
• 8 labyrinths with only pseudo double-barriers
• 48 labyrinths with real and pseudo double-barriers

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## 1 thought on “The Labyrinths with 3 Pseudo Double-barriers, 4 Arms, and 5 Circuits”

1. Pingback: Pseudo Single Barrier | blogmymaze

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