With the exception of group 19, all groups that have all pendant values and top cord value present show the following relationship:
\[ \sum\limits_{j=1}^4 P_{ij} = \sum\limits_{j=5}^8 P_{ij} = \frac{top\_value}{2}\;\;\;for\;(i=13,15,16,17,18,21,22,23,24) \]
Where one of the three parts of the relationship is unknown due to breakage, the other two still appear:
\[ \sum\limits_{j=1}^4 P_{ij} = \sum\limits_{j=5}^8 P_{ij} = \frac{top\_value}{2}\;\;\;for\;(i=12,14,17) \]
\[ \sum\limits_{j=1}^4 P_{ij} = \frac{top\_value}{2}\;\;\;for\;(i=9) \]
\[ \sum\limits_{j=5}^8 P_{ij} = \frac{top\_value}{2}\;\;\;for\;(i=2,10,11) \]
(Note: P_{ij} is the value of the j^{th} pendant in the i^{th} group.)
Groups 17 and 19 both have the same relationship among the first 4 pendants:
\[ P_{1} = P_{2} = \frac{x}{4} + 3 \]
\[ P_{3} = \frac{x}{4} + 4 \]
\[ P_{4} = \frac{x}{4} - 10 \]
And as a result:
\[ P_{1}+P_{2} = \frac{x}{2} + 6,\;\;\;\;\;\;\;P_{3}+P_{4} = \frac{x}{2} - 6\]
For group 17, where X=100 and for group 19, where X=112.
Since group 19 is the only group for which P1 + P2 + P3 + P4 ≠ P5 + P6 + P7 + P8, it is interesting to note that also:
\[ P_{1}+P_{2}+P_{3}+P_{4} = \frac{top\_value}{2}-6\;\;\;where\;\frac{top\_value}{2}\;is\;rounded\;DOWN \]
\[ P_{5}+P_{6}+P_{7}+P_{8} = \frac{top\_value}{2}+6\;\;\;where\;\frac{top\_value}{2}\;is\;rounded\;UP \]