KH0156/UR1140, AS140/N9 - Pendant Pendant Sums

Note: The pendant order on the listing proceeds from one end of the bar to the other, goes around the end, and continues on the other side. However, similar color and number patterns are found in both parts if the pendants are read instead from one end of the bar to the other, and then beginning at the original end on the other side of the bar. We will, therefore, refer to the pendants and groups on side 2 as if following the second scenario. Part 1 is pendants 1--->90 and references to the j^th pendant in the i^th group correspond to pendant 9 (i-1) +j. Part 2 is pendants 180--->91 and references to the j^th pendant in the i^th group correspond to pendant 190-9i-j.

By color, each part is separated into 2 subparts of 6 groups and 4 groups respectively. Each group has the same color pattern: 5 B, 2 mixed, 2 B. In the first 6 groups in part 1, the 2 mixed cords are B:BB/B, and in the last 4 groups they are B:BB. In the first 6 groups in part 2, the 2 mixed cords are B:BB, and in the last 4 groups they are B:G.

1. The last pendant in each group has the maximum value.
2. With the exception of group 10 in part 1, the value on pendant 7 is always great than the value on pendant 8.

1. For the 6 groups of the first subpart, the sum of the values in the 5th position equals the sum of the values in the 4th position. That is:
   
   \[ \sum\limits_{i=1}^{6} P_{i5} = \sum\limits_{i=1}^{6} P_{i6} \]
2. For the 4 groups of the second subpart, the sum of the values in the first position equals the sum of the values in the second position.
   
   \[ \sum\limits_{i=7}^{10} P_{i1} = \sum\limits_{i=7}^{10} P_{i2} \]
3. Excluding the last pendant in each group, the sum of the values in the first group equals the sum of the values in the corresponding group in the second subpart (group 7).
   
   \[ \sum\limits_{j=1}^{8} P_{1j} = \sum\limits_{j=1}^{8} P_{7j} \]