Choose the correct one

Sequences built from clusters of dots follow a fixed triple rule: as the figures progress, the size of each cluster grows by one, the total number of dots falls by one, and the dots split as evenly as possible between filled (shaded) and hollow (unshaded), with a single leftover dot always shaded.

• Cluster-size rule: figure n groups its dots into clusters of size n; any dots that do not fill a complete cluster form one smaller leftover cluster.

• Count rule: the total number of dots drops by exactly one from each figure to the next.

• Shading rule: shaded and unshaded dots are split as evenly as possible - exactly half and half when the total is even, with the single extra dot shaded when the total is odd.

Applying this to the five given figures:

1. Figure 1: 19 individual dots (clusters of size 1).

2. Figure 2: 18 dots in 9 clusters of size 2.

3. Figure 3: 17 dots in 5 clusters of size 3 plus one leftover cluster of 2.

4. Figure 4: 16 dots in 4 clusters of size 4.

5. Figure 5: 15 dots in 3 clusters of size 5.

The missing sixth figure must continue both trends: cluster size 6, and a total of 15 - 1 = 14 dots. Since 14 does not divide evenly by 6 (6 + 6 = 12, with 2 left over), it must show two clusters of six plus one leftover cluster of two - and because 14 is even, exactly 7 dots must be shaded and 7 unshaded.

Among the five candidate figures, only the one with fourteen total dots arranged as two clusters of six plus a leftover pair - split exactly seven shaded and seven unshaded - satisfies all three rules simultaneously; the others each break at least one rule (a total that does not fall to fourteen, clusters that skip past size six, or no leftover cluster at all).