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Brainteaser -
 A Hands-on Enneagram-Construction Puzzle

© John Fudjack - February, 1998

In this short paper, we invite the reader to solve three closely related visual puzzles that demonstrate some of the principles underlying the construction of the Enneagram as a geometrical figure. It will take a few short paragraphs to set the puzzle up - so please bear with us.

In 1995, Pat and I offered a theory about the relationship between the Enneagram and the MBTI. On the basis of the descriptions associated with each Enneatype and each MBTI type, we assigned one of the eight Jungian Types to each of the Enneagram Points, as a 'prototype'. For instance, we identified Jung's 'extraverted feeling type', EF, as prototypical of Enneagram Point Two. As most readers will know, there are two MBTI types that comprise this Jungian group - the ENFJ and the ESFJ - so, in effect, we had assigned two MBTI types to Enneagram Point Two as 'prototypical' of it. We conceived of all of the MBTI J-Types as 'prototypical' of Enneagram Point One, which was the only Point that we believed to be different. Here are the remaining prototypes that we came up with at that time: IF-1, EF-2, ES-3, IN-4, IT-5, IS-6, EN-7, and ET-8. As it turns out, these prototypes acted as very good predictors of how the MBTI types would distribute across the Enneagram. 1


Figure One
It then occured to us to try to see how the Jungian/MBTI prototypes physically stood in relationship to each other when placed, according to the way we had assigned them, on the geometrical figure that we know as the Enneagram. We naturally wondered if similar Jungian types might take up adjacent positions on the Enneagram, or bunch together in some other way that demonstrated a pattern. So we decided to label each of the points on the nine-pointed diagram with its associated prototype, which resulted in the diagram that you see in Figure One to the left.

At first it looked like the Jungian prototypes were randomly placed. But then it occured to us to treat the eight Jungian types as four pairs, comprising what are called the four 'core' types in the MBTI - feeling types, thinking types, intuitive types, and sensing types. In order to do this, we simply connected the dots between IF and EF, and so forth, on the diagram. Figure Two, which you see below, was the result -


Figure Two

To our surprise, the diagram that emerged was a symmetrical one! It is easier to see this when the diagram is rotated one place to the left, as follows -


Figure Three

Figure Four

Figure Five

The figure that emerged when we connected the dots is symmetrical with respect to the vertical axis represented by the pink line in Figure Four above. It has only 'one degree' of symmetry, a 'left-right' symmetry. There is no 'top-bottom' symmetry, as you can see if you run a horizontal line through the center of the circle, as we have done in Figure Five.

Now you are ready to do the puzzles.

Puzzle One

In Figure Four above, as we have mentioned, the figure is symmetrical in only ONE way - it has left-right symmetry, but not top-bottom symmetry. By adding to Figure Five no more than 8 straight lines that connect one Enneagram Point to another, create a figure that has THREE degrees of symmetry. In other words, the figure that you draw should not only be left-right symmetrical, but also symmetrical with respect to two other imaginary lines (axes) passing through the center point of the circle. [This is not a trick question, by the way - there IS an answer]

When you are ready, click here for the answer.

ANSWER to First Puzzle:

Figure Six, below, shows the figure. The pink lines in Figure Seven illustrate the three axes with respect to which the figure is symmetrical. By the way, can you find the three five-pointed stars that appear in the figure?


Figure Six

Figure Seven

Puzzle Two

Now here is the second Puzzle - In Figure Six, by removing no more than three straight lines connecting Enneapoints, make a figure in which each Enneapoint is connected by straight lines to two other Enneapoints and ONLY two. There are only TWO different families of solution to this puzzle, rendering two essentially different designs. Can you find BOTH?

When you are ready, click here for the answer.

ANSWER to Second Puzzle:


Figure Eight

Figure Nine
Figure Ten

Figure Eight is the shape that we know as 'the Enneagram'! It has nine straight lines that connect the points on the circle and is made up of two superimposed figures - an equilateral triangle and a complex figure connecting the six remaining points. Figure Nine also has nine straight lines connecting the points on the circle. It is a figure which, in a previous paper, I have described as illustrating a hidden structure that is 'latent' within the Enneagram. It is made up of three figures - identical equilateral triangles. Like Figure Six, it has three degrees of symmetry, and is thus highly symmetrical. Symmetry, in illustrations, represents harmony - as Jung points out in his discussion of mandala figures.

Figure Ten is the central figure in the Guhya-Kali Yantra, used for meditation. It is related to one of the nine esoteric aspects of Kali, according to Madhu Khanna 2, and includes the figure that we see in Figure Nine, comprised of three equilateral triangles.

Third Puzzle

Here's the third puzzle -

Figure Eleven
Figure Eight and Figure Nine above have in common the fact that each straight line connects two and only two points. Using nine straight lines, can you connect the points in Figure Eleven in such a way that you construct another figure that has three degrees of symmetry, with each point connected by straight lines to two and only two other points?

When you are ready, click here for the answer.

ANSWER to Third Puzzle:


Figure Twelve

Here is one answer. Like Figures Eight and Nine, Figure Twelve has nine straight lines connecting the nine points on the circle. Like the Enneagram (Figure Eight), it is made up of two superimposed shapes, one of which is the same equilateral triangle that appears in the Enneagram. But the second shape is highly symmetrical. Like Figure Nine, it has three degrees of symmetry. This illustrates that if the creator of the Enneagram-figure had wanted to, he or she could easily have drawn a symmetrical nine-lined figure combining two superimposed shapes, one of which was the same central equilateral triangle. By choosing NOT to do so, what kind of statement was he/she making?

We address this question in detail in a series of articles, entitled Revisiting the Relationship Between the MBTI and the Enneagram, which begins in this issue of the Journal. In Part II of this series the Enneagram is compared to the Shri Yantra, a profound geometrical design from India. Like Figure Twelve, the Shri Yantra has the superficial appearance of being made up of interpenetrating upward and downward-pointing triangles. But it also shares with the Enneagram something that it does not share with Figure Twelve - both have been cleverly constructed so as to incorporate a central asymmetry into the design, the significance of which is explored in Part II of the series.

Another Puzzle?

Interested in doing one more puzzle? A well-known authority on the Enneagram believes the following two figures to be significantly related to the figure that we know as the Enneagram (Figure Eight). Can you describe what that relationship is? Email us your answer by clicking here (The solution to this puzzle will be revealed in the above-mentioned series.)


Figure Thirteen

Figure Fourteen
Footnotes

1. A Brief Review and Update, John Fudjack, January 1998, 'The Enneagram and the MBTI'.
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1. Madhu Khanna, Yantra: The Tantric Symbols of Cosmic Unity, Thames and Hudson, 1979, footnote 81.
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